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Expanded Kaleido-Facetings

In February 2014 a noteworthy combination from

was brought up by W. Gevaert. In the sequel a vivid research for class members of according CRFs was initiated, which then provided several so far unknown "crown jewels".

Gevaert himself also elaborated some of the first known examples, but then he reduced to just outline his ideas and contribute to combinatorics. Quickfur, "student5", and Četrnáct also found some further individual examples. A more systematical research with several more finds and esp. the concrete cell evaluation of all known cases then has been done by Klitzing. (Therefore the following content mostly is original work.)

For kaleidoscopical construction usually a seed point within the fundamental domain is used. Its reflection all over the mirror symmetry then constructs the vertex set of the to be designed polytope. Obviously an other such vertex outside the domain likewise could be used, again providing the same vertex set – but then other elements in the dimensions beyond. Generally these such derived polytopes then will be facetings of the former polytope. If esp. that point was taken to be a direct mirror image of that point within, then that edge, which is derived as the hull of these 2 points, gets just inverted.

If one wonders what these kaleido-faceted polytopes would look like in terms of their Dynkin diagram, then clearly some edges, i.e. node symbols which formerly had prograde unit size, now will have retrograde unite size. That is, some x just gets reflected into a (-x). But because faces, which stay within their face planes, keep their neighbouring vertices still being connected, the other edges accordingly will get elongated thereby by the amount of a vertex figure, i.e. by the corresponding shortchord.

 

Assume we start with any (sub)diagram x-n/m-y (where y is just any length edge, possibly zero), then by flipping that x into (-x) we elongate the neighbouring edge from size y into y+cos(π m/n)x. Moreover, if we start with some layered starting figure, then such an edge flip could be applied independently in any layer. We just have to check, that still any layer can be connected by unit-lacings to at least one of the other layers. For its converse cf. †).

Obviously retrograde edges would not be allowed in CRF polytopes. To that aim a corresponding Stott expansion will come in, which then adds one unit to the respective node position – uniformely within all layers. Sometimes longer edges also would occur within the symbols of individual layers. Here we have to check then that those "edges" become just false ones (pseudo edges), burried somewhere within. E.g. covered by inter-layer lacing elements. For its converse cf. ‡).

Besides of the former exclusions we still have to check for the regularity of all the polygonal faces (of the total figure).


One of the most common cases wrt. ‡) can already be filtered out a priori: When considering convex starting polytopes which become displayed as mere lace towers, i.e. when keeping the layer heights throughout all the transformations, then mixtures of prograde and retrograde edges at the same node would not be allowable. This is because we have to apply a Stott expansion to the retrograde edges, bringing these edges then back to zero size. But this same expansion would double up simultanuously the prograde edges at the same node. Generally speaking, an inner-layer edge of size u = 2x might be allowable, e.g. as the equator of an hexagon. But within the reach of the given preconditions the 2 adjoined "halves" would not be co-planar before the expansion, and so by mere parallel translation cannot become thereafter.

This same argument surely serves valid for full dimensional subsymmetries which are cartesian products, provided all transformations affect only one cartesian component, while the other keeps unchanged. (This then would be the generalization of unchanged heights.) Even changes in more than one component are compensated here, provided this change can be split into independent changes in either affected component each.

Wrt. mere lace towers we likewise have an a priori restriction: lacing triangles freely can be affected by edge reversals, so can squares only if both parallel edges are affected simultanuously, but any other 2D face can not. Nor could any face be elongated within its face plain by later partial Stott expansions, except of those which do respect the full symmetry of that polygon.

†) - Layers fall apart into subsets: at least one layer cannot be connected to none of the other ones by unit inter-layer lacings. Or dead ends will arise: vertices of at least one non-extremal layer wrt. some axial orientation do not allow for unit inter-lacings to any higher (or lower) vertex.
‡) - At least one non-unit inner-layer edge survives at the outside.
°) - Asks for some non-regular polygonal faces.


3D EKF:

EKF of the icosahedron
EKF of the small rhombicuboctahedron
EKF of the cuboctahedron

4D EKF:

EKF of the icosahedral pyramid
EKF of the hexacosachoron
EKF of the icositetrachoron
EKF of the hexadecachoron
EKF of the pentachoron
EKF of the small rhombated pentachoron
EKF of the small prismatodecachoron
EKF of the rectified hexacosachoron
EKF of the small prismated icositetrachoron
EKF of the snub (dis)icositetrachoron
EKF of the rectified tesseract


EKF of the icosahedron (x3o5o)

©

in o2o2o subsymmetry   (up)
Representation:
xof 2 fxo 2 ofx &#zx  (ike)
    = xofox 2 ofxfo &#xt
All layers &
kaleido-facetings per layer:
A:  x 2 f 2 o   →  A1:  (-x) 2   f  2   o
B:  o 2 x 2 f   →  B2:    o  2 (-x) 2   f
C:  f 2 o 2 x   →  C3:    f  2   o  2 (-x)
A priori invalid combinations:
none
Other layer-combinations:
A1:     (-x)of 2 fxo 2 ofx &#zx
A1B2:   (-x)of 2 f(-x)o 2 ofx &#zx     → †)
A1B2C3: (-x)of 2 f(-x)o 2 of(-x) &#zx  → †)
Stott expansion:
(derived potential CRFs)
oxF 2 fxo 2 ofx &#zx  (bilbiro, J91)
    = oxFxo 2 ofxfo &#xt

in . o3o subsymmetry   (up)
Representation:
xofo 3 ofox &#xt  (ike)
All layers &
kaleido-facetings per layer:
A:  x 3 o   →  A1:  (-x) 3   x
B:  o 3 f
C:  f 3 o
D:  o 3 x   →  D2:    x  3 (-x)
A priori invalid combinations:
A1 + D2  → ‡) (u in A, u in D)
Other layer-combinations:
A1:    (-x)ofo 3 xfox &#xt
Stott expansion:
(derived potential CRFs)
oxFx 3 xfox &#xt  (thawro, J92)
 
 
 
 
 
 
 
 
 
 
 
 

in . o5o subsymmetry   (up)
Representation:
oxoo 5 ooxo &#xt  (ike)
All layers &
kaleido-facetings per layer:
A:  o 5 o
B:  x 5 o   →  B1:  (-x) 5   f
C:  o 5 x   →  C2:    f  5 (-x)
D:  o 5 o
A priori invalid combinations:
none
Other layer-combinations:
B1:    o(-x)oo 5 ofxo &#xt
B1C2:  o(-x)fo 5 of(-x)o &#xt  → †)
Stott expansion:
(derived potential CRFs)
xoxx 5 ofxo &#xt  (pocuro, J32)

related: ..xx 5 ..xo &#xt  (pecu, J5)
related: xox. 5 ofx. &#xt  (pero, J6)
 
 
 
 
 
 
 
 
 
 
 
 
 


EKF of the small rhombicuboctahedron (x3o4x)

©

in o3o3o subsymmetry   (up)
Representation:
qo 3 xx 3 oq &#zx  (sirco)
All layers &
kaleido-facetings per layer:
A:  q 3 x 3 o   →  A2:    w  3 (-x) 3   x   →  A23:    w  3   o  3 (-x)
B:  o 3 x 3 q   →  B2:    x  3 (-x) 3   w   →  B21:  (-x) 3   o  3  w
A priori invalid combinations:
A + B2  → ‡ (u in A)
A2 + B  → ‡ (u in B)
Other layer-combinations:
B21:    q(-x) 3 xo 3 ow &#zx     → †)
A2B2:   wx 3 (-x)(-x) 3 xw &#zx
A2B21:  w(-x) 3 (-x)o 3 xw &#zx  → †)
A23B21: w(-x) 3 oo 3 (-x)w &#zx  → †)
Stott expansion:
(derived potential CRFs
& beyond)
1:-: wx 3 xx 3 oq &#zx
  → °) (asks for non-regular hexagons: wx .. oq &#zx)
  = non-Johnsonian (patex sirco)
(-2):-: qo 3 oo 3 oq &#zx
  = Wythoffian o3o4x (cube)
13:-: wx 3 xx 3 xw &#zx
  = Wythoffian x3x4x (girco)
1(-2)3:-: wx 3 oo 3 xw &#zx
  = Wythoffian o3x4x (tic)
2:A2B2: wx 3 oo 3 xw &#zx
  = Wythoffian o3x4x (tic)
(-1)2:A2B2: qo 3 oo 3 xw &#zx
  → °) (asks for non-regular hexagons: qo .. xw &#zx)
  = non-Johnsonian (patex cube)
(-1)2(-3):A2B2: qo 3 oo 3 oq &#zx
  = Wythoffian o3o4x (cube)
 

in o2o4o subsymmetry   (up)
Representation:
wx 2 xx 4 ox &#zx  (sirco)
All layers &
kaleido-facetings per layer:
A:  w 2 x 4 o   →  A2:    w  2 (-x) 4   q
B:  x 2 x 4 x   →  B1:  (-x) 2   x  4   x   →  B12:  (-x) 2 (-x) 4   w
                                            ↳  B13:  (-x) 2   w  4 (-x)
                ↳  B2:    x  2 (-x) 4   w   →  (B21 = B12)
                ↳  B3:    x  2   w  4 (-x)  →  (B31 = B13)
A priori invalid combinations:
A + B2,B12  → ‡ (u in A)
A2  → ‡ (q or w in extremal layer, i.e. A)
Other layer-combinations:
B1:  w(-x) 2 xx 4 ox &#zx     → †)
B3:  wx 2 xw 4 o(-x) &#zx
B13: w(-x) 2 xw 4 o(-x) &#zx  → †)
Stott expansion:
(derived potential CRFs
& beyond)
(-1):-: qo 2 xx 4 ox &#zx   (squobcu, J28)
(-2):-: wx 2 oo 4 ox &#zx   (esquidpy, J15)
(-1)(-2):-: qo 2 oo 4 ox &#zx
  = Wythoffian x3o4o (oct)
3:B3: wx 2 xw 4 xo &#zx
  = Wythoffian o3x4x (tic)
(-1)3:B3: qo 2 xw 4 xo &#zx
  → °) (asks for non-regular hexagons: qo 2 xw &#zx)
  = non-Johnsonian (pactic)
(-2)3:B3: wx 2 oq 4 xo &#zx
  → °) (asks for non-regular hexagons: wx 2 oq &#zx)
  = non-Johnsonian (pexco)
(-1)(-2)3:B3: qo 2 oq 4 xo &#zx
  = Wythoffian o3x4o (co)
 
in . o4o subsymmetry   (up)
Representation:
xxxx 4 oxxo &#xt  (sirco)
additional,
not prismatically symmetric
combinations of formers:
none, because A2 was ruled out already, and the possible combinations B1 + B3, B1 + B13, and B3 + B13 
within the 2 medial layers B each would ask for u-edges there → ‡)

in . o3o subsymmetry   (up)
Representation:
xxwoqo 3 oqowxx &#xt  (sirco)
All layers &
kaleido-facetings per layer:
A:  x 3 o   →  A1:  (-x) 3   x   →  A12:    o  3 (-x)
B:  x 3 q   →  B1:  (-x) 3   w
C:  w 3 o
D:  o 3 w
E:  q 3 x   →  E2:    w  3 (-x)
F:  o 3 x   →  F2:    x  3 (-x)  →  F21:  (-x) 3   o
A priori invalid combinations:
A   + B1,F21   → ‡ (u in A)
A1  + B,E2,F2  → ‡ (u in A)
A12 + E,F      → ‡ (u in A)
B   + F21      → ‡ (u in F)
B1  + F2       → ‡ (u in F)
E   + F2       → ‡ (u in F)
E2  + F        → ‡ (u in F)
Other layer-combinations:
E2F2       xxwowx 3 oqow(-x)(-x) &#xt
A1B1F21    (-x)(-x)woq(-x) 3 xwowxo &#xt     → †)
A12B1E2F21 o(-x)wow(-x) 3 (-x)wow(-x)o &#xt  → †)
Stott expansion:
(derived potential CRFs
& beyond)
1:E2F2: xxwowx 3 xwxQoo &#xt
  → °) (asks for non-unit edges DC, DE, DF)

related: xxw.wx 3 xwx.oo &#xt
  → °) (asks for non-regular hexagons: ... xwx &#xt)


EKF of the cuboctahedron (o3x4o)

©

in o3o3o subsymmetry   (up)
Representation:
x3o3x  (co)
All layers &
kaleido-facetings per layer:
A: x3o3x  →  A1: (-x)3 x 3  x   →  A12:   o 3(-x)3  u
                                ↳  A13: (-x)3  u 3(-x)
          ↳  A3:   x 3 x 3(-x)  →  (A31 = A13)
                                ↳  (A32 = A23)
A priori invalid combinations:
A12, A13  → ‡ (u in A)
Stott expansion:
(derived potential CRFs)
(-1):-: o3o3x
  = Wythoffian (tet)
2:-: x3x3x
  = Wythoffian (toe)
(-1)2:-: o3x3x
  = Wythoffian (tut)
(-1)2(-3):-: o3x3o
  = Wythoffian (oct)
1:A1: o3x3x
  = Wythoffian (tut)
1(-2):A1: o3o3x
  = Wythoffian (tet)
1(-3):A1: o3x3o
  = Wythoffian (oct)
 

in o2o4o subsymmetry   (up)
Representation:
qo 2 xo 4 oq &#zx  (co)
All layers &
kaleido-facetings per layer:
A: q2x4o  →  A2: q 2(-x)4 q
B: o2o4q
A priori invalid combinations:
A2  → ‡ (q in A)
Stott expansion:
(derived potential CRFs
& beyond)
1:-: wx 2 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: wx .. oq &#zx)
  = non-Johnsonian (pexco)
3:-: qo 2 xo 4 xw &#zx
  → °) (asks for non-regular hexagons: qo .. xw &#zx)
  = non-Johnsonian (pactic)
13:-: wx 2 xo 4 xw &#zx
  = Wythoffian o3x4x (tic)
 
in . o4o subsymmetry   (up)
Representation:
xox 4 oqo &#xt  (co)
additional,
not prismatically symmetric
combinations of formers:
none, because A2 was disallowed and thus no independent changes in extremal layers A remain possible.

in o2o2o subsymmetry   (up)
Representation:
qoq 2 qqo 2 oqq &#zx  (co)
All layers &
kaleido-facetings per layer:
A: q2q2o
B: o2q2q
C: q2o2q

(As this representation does not show up (true / x-) edges within the layers, those thus cannot be inverted either. 
Therefore at most pure partial Stott expansions wrt. this subsymmetry remain possible.)
Stott expansion:
(derived potential CRFs)
1:-: wxw 2 qqo 2 oqq &#zx
  → °) (asks for non-regular hexagons: wx .. oq &#zx)
  = non-Johnsonian (pexco)
12:-: wxw 2 wwx 2 oqq &#zx
  → °) (asks for non-regular hexagons: wx .. oq &#zx)
  = non-Johnsonian (pactic)
123:-: wxw 2 wwx 2 xww &#zx
  = Wythoffian o3x4x (tic)
 

in . o3o subsymmetry   (up)
Representation:
xxo 3 oxx &#xt  (co)
All layers &
kaleido-facetings per layer:
A: x3o  →  A1: (-x)3x  →  A12: o3(-x)
B: x3x  →  B1: (-x)3u
        ↳  B2: u3(-x)
C: o3x  →  C2: x3(-x)  →  C21: (-x)3o
A priori invalid combinations:
A   + B1,C21  → ‡ (u in A)
A1  + B2,C2   → ‡ (u in A)
A12 + B,C     → ‡ (u in A)
B   + C2,C21  → ‡ (u in B)
B1  + C2      → ‡ (u in C)
B2  + C       → ‡ (u in C)
Other layer-combinations:
C2       xxx 3 ox(-x) &#xt  → †)
B2C2     xux 3 o(-x)(-x) &#xt
A1C21    (-x)x(-x) 3 xxo &#xt  → †)
A1B1C21  (-x)(-x)(-x) 3 xuo &#xt  → †)
A12B1C21 o(-x)(-x) 3 (-x)uo &#xt  → †)
Stott expansion:
(derived potential CRFs)
2:AB2C2: xux 3 xoo &#xt
  = Wythoffian o3x3x (tut)


EKF of the icosahedral pyramid (ox3oo5oo&#x)

©

Obviously here at most those subsymmetries can be applied, which do respect the possibilities of the base polyhedron, i.e. of the icosahedron (cf. above). As it turns out, all three types become positively applicable.

in . o2o2o subsymmetry   (up)
Representation:
xof 2 fxo 2 ofx &#zx || o2o2o  (ikepy)
    = xofox 2 ofxfo &#xt || o2o
 ©
All layers &
kaleido-facetings per layer:
A:  x 2 f 2 o   →  A1:  (-x) 2   f  2   o
B:  o 2 x 2 f   →  B2:    o  2 (-x) 2   f
C:  f 2 o 2 x   →  C3:    f  2   o  2 (-x)
D:  o 2 o 2 o
A priori invalid combinations:
none
Other layer-combinations:
A1:     (-x)of 2 fxo 2 ofx &#zx || o2o2o
A1B2:   (-x)of 2 f(-x)o 2 ofx &#zx || o2o2o     → †)
A1B2C3: (-x)of 2 f(-x)o 2 of(-x) &#zx || o2o2o  → †)
Stott expansion:
(derived potential CRFs)
oxF 2 fxo 2 ofx &#zx || x2o2o
    = oxFxo 2 ofxfo &#xt || x2o
    = bilbiro || line
    
  → CRF with cell list:
        1 bilbiro (J91)
        4 peppies (J2)
        4 squippies (J1)
        4 tets
        2 trips

in . . o3o subsymmetry   (up)
Representation:
xofo 3 ofox &#xt || o3o  (ikepy)
 ©
All layers &
kaleido-facetings per layer:
A:  x 3 o   →  A1:  (-x) 3   x
B:  o 3 f
C:  f 3 o
D:  o 3 x   →  D2:    x  3 (-x)
E:  o 3 o
A priori invalid combinations:
A1 + D2  → ‡) (u in A, u in D)
Other layer-combinations:
A1:    (-x)ofo 3 xfox &#xt || o3o
Stott expansion:
(derived potential CRFs)
oxFx 3 xfox &#xt || x3o
    = thawro || {3}
    
  → CRF with cell list:
        1 oct
        3 peppies (J2)
        3 squippies (J1)
        9 tets
        1 thawro (J92)
        1 tricu (J3)
        3 trips

in . . o5o subsymmetry   (up)
Representation:
oxoo 5 ooxo &#xt || o5o  (ikepy)
 ©
All layers &
kaleido-facetings per layer:
A:  o 5 o
B:  x 5 o   →  B1:  (-x) 5   f
C:  o 5 x   →  C2:    f  5 (-x)
D:  o 5 o
E:  o 5 o
A priori invalid combinations:
none
Other layer-combinations:
B1:    o(-x)oo 5 ofxo &#xt || o5o
B1C2:  o(-x)fo 5 of(-x)o &#xt || o5o  → †)
Stott expansion:
(derived potential CRFs)
xoxx 5 ofxo &#xt || x5o
    = pocuro || {5}
    
  → CRF with cell list:
        5  peppies (J2)
        2  pips
        1  pocuro (J32)
        10 squippies (J1)
        5  tets
        5  trips

related: xox. 5 ofx. &#xt || x5o
    = pero || {5}
    
  → CRF (segmentochoron) with cell list:
        1  pecu (J5)
        5  peppies (J2)
        1  pero (J6)
        1  pip
        10 squippies (J1)


EKF of the hexacosachoron (x3o3o5o)

©

in o2o3o5o subsymmetry   (up)
Representation:
VFfxo 2 oxofo 3 oooox 5 ooxoo &#zx  =  oxofofoxo 3 ooooxoooo 5 ooxoooxoo &#xt  (ex)
All layers &
kaleido-facetings per layer:
A:  V2o3o5o
B:  F2x3o5o   →  B2:   F 2(-x)3  x 5  o   →  B23:   F 2  o 3(-x)5  f
C:  f2o3o5x   →  C4:   f 2  o 3  f 5(-x)
D:  x2f3o5o   →  D1: (-x)2  f 3  o 5  o
E:  o2o3x5o   →  E3:   o 2  x 3(-x)5  f   →  E32:   o 2(-x)3  o 5  f
A priori invalid combinations:
when component 1 (o2.3.5.) remains unchanged (no D1):
  B2 + E3                   → ‡) (u in B, u in E)
  E32 + neither B2 nor B23  → ‡) (u in B)
  B23 + neither E3 nor E32  → ‡) (u in E)

when component 2 (.2o3o5o) remains unchanged (neither B2, B23, C4, E3, E32):
  none

As changes in (o2.3.5.) do not affect (.2o3o5o) and vice versa,
the above exclusions remain valid too, when D1 is activ.
Other layer-combinations:
D1:         VFf(-x)o 2 oxofo 3 oooox 5 ooxoo &#zx
B2:         VFfxo 2 o(-x)ofo 3 oxoox 5 ooxoo &#zx  → †)
B2E32:      VFfxo 2 o(-x)of(-x) 3 oxooo 5 ooxof &#zx
E3:         VFfxo 2 oxofx 3 oooo(-x) 5 ooxof &#zx
B23E3:      VFfxo 2 ooofx 3 o(-x)oo(-x) 5 ofxof &#zx
C4:         VFfxo 2 oxofo 3 oofox 5 oo(-x)oo &#zx
B2D1:       VFf(-x)o 2 o(-x)ofo 3 oxoox 5 ooxoo &#zx
B2D1E32:    VFf(-x)o 2 o(-x)of(-x) 3 oxooo 5 ooxof &#zx  → †)
D1E3:       VFf(-x)o 2 oxofx 3 oooo(-x) 5 ooxof &#zx
B23D1E3:    VFf(-x)o 2 ooofx 3 o(-x)oo(-x) 5 ofxof &#zx
C4D1:       VFf(-x)o 2 oxofo 3 oofox 5 oo(-x)oo &#zx
B23E32:     VFfxo 2 ooof(-x) 3 o(-x)ooo 5 ofxof &#zx  → †)
B2C4:       VFfxo 2 o(-x)ofo 3 oxfox 5 oo(-x)oo &#zx
B2C4E32:    VFfxo 2 o(-x)of(-x) 3 oxfoo 5 oo(-x)of &#zx  → †)
C4E3:       VFfxo 2 oxofx 3 oofo(-x) 5 oo(-x)of &#zx
B23D1E32:   VFf(-x)o 2 ooof(-x) 3 o(-x)ooo 5 ofxof &#zx  → †)
B2C4D1:     VFf(-x)o 2 o(-x)ofo 3 oxfox 5 oo(-x)oo &#zx
B2C4D1E32:  VFf(-x)o 2 o(-x)of(-x) 3 oxfoo 5 oo(-x)of &#zx  → †)
C4D1E3:     VFf(-x)o 2 oxofx 3 oofo(-x) 5 oo(-x)of &#zx  → †)
B23C4D1E3:  VFf(-x)o 2 ooofx 3 o(-x)fo(-x) 5 of(-x)of &#zx  → †)
B23C4E32:   VFfxo 2 ooof(-x) 3 o(-x)foo 5 of(-x)of &#zx  → †)
B23C4D1E32: VFf(-x)o 2 ooof(-x) 3 o(-x)foo 5 of(-x)of &#zx   → †)
Stott expansion:
(derived potential CRFs)
1:D1: BAFox 2 oxofo 3 oooox 5 ooxoo &#zx
  = oxoofooxo 3 oooxoxooo 5 ooxoooxoo &#xt
  → CRF with cell list:
        24  ikes
        60  squippies (J1)
        180 tets
        20  trips

related: ..Fox 2 ..ofo 3 ..oox 5 ..xoo &#zx
  = ..oofoo.. 3 ..oxoxo.. 5 ..xooox.. &#xt
  → CRF with cell list:
        2  does
        24 gyepips (J11)
        60 squippies (J1)
        40 tets
        20 trips

related: ...ox 2 ...fo 3 ...ox 5 ...oo &#zx
  = ...ofo... 3 ...xox... 5 ...ooo... &#xt (twau iddip)
  → CRF with cell list:
        2  ids
        24 peppies (J2)
        60 squippies (J1)
        20 trips
2:B2E32: VFfxo 2 xoxFo 3 oxooo 5 ooxof &#zx
  = xoxFoFxox 3 oxoooooxo 5 ooxofoxoo &#xt
  → CRF with cell list:
        30 bilbiroes (J91)
        26 ikes
        80 octs
        60 squippies (J1)
        40 tets

related: ..fxo 2 ..xFo 3 ..ooo 5 ..xof &#zx
  = ..xFoFx.. 3 ..ooooo.. 5 ..xofox.. &#xt
  → CRF with cell list:
        30 bilbiroes (J91)
        24 peppies (J2)
        2  srids
        40 tets
3:E3: VFfxo 2 oxofx 3 xxxxo 5 ooxof &#zx
  = oxofxfoxo 3 xxxxoxxxx 5 ooxofoxoo &#xt
  → CRF with cell list:
        2   ids
        30  ikes
        40  octs
        60  pips
        180 squippies (J1)
        180 tets
        80  tricues (J3)
        120 trips

related: ..fxo 2 ..ofx 3 ..xxo 5 ..xof &#zx
  = ..ofxfo.. 3 ..xxoxx.. 5 ..xofox.. &#xt
  → CRF with cell list:
        30  ikes
        40  octs
        24  pecues (J5)
        12  pips
        180 squippies (J1)
        2   tids
3:B23E3: VFfxo 2 ooofx 3 xoxxo 5 ofxof &#zx
  = ooofxfooo 3 xoxxoxxox 5 ofxofoxfo &#xt
  → CRF with cell list:
        2   ids
        40  ikes
        40  octs
        12  pips
        24  pocuroes (J32)
        180 squippies (J1)
        80  tets

related: ..fxo 2 ..ofx 3 ..xxo 5 ..xof &#zx
  = ..ofxfo.. 3 ..xxoxx.. 5 ..xofox.. &#xt
  → CRF with cell list:
        30  ikes
        40  octs
        24  pecues (J5)
        12  pips
        180 squippies (J1)
        2   tids
4:C4: VFfxo 2 oxofo 3 oofox 5 xxoxx &#zx
  = oxofofoxo 3 oofoxofoo 5 xxoxxxoxx &#xt
  → CRF with cell list:
        2   does
        40  ikes
        60  pips
        300 squippies (J1)
        100 tets
        120 trips

related: .Ffxo 2 .xofo 3 .ofox 5 .xoxx &#zx
  = .xofofox. 3 .ofoxofo. 5 .xoxxxox. &#xt
  → CRF with cell list:
        40  ikes
        36  pips
        300 squippies (J1)
        2   srids
        60  tets
        60  trips
12:B2D1: BAFox 2 xoxFx 3 oxoox 5 ooxoo &#zx
  = xoxxFxxox 3 oxoxoxoxo 5 ooxoooxoo &#xt
  → CRF with cell list:
        48  gyepips (J11)
        20  hips
        2   ikes
        80  octs
        120 squippies (J1)
        40  tricues (J3)
        60  trips

related: ...ox 2 ...Fx 3 ...ox 5 ...oo &#zx
  = ...xFx... 3 ...xox... 5 ...ooo... &#xt (twau tipe)
  → CRF with cell list:
        20 hips
        24 peppies (J2)
        60 squippies (J1)
        2  ties
13:D1E3: BAFox 2 oxofx 3 xxxxo 5 ooxof &#zx
  = oxoxfxoxo 3 xxxoxoxxx 5 ooxfofxoo &#xt
  → CRF with cell list:
        30  bilbiroes (J91)
        2   ids
        40  octs
        24  pips
        24  pocuroes (J32)
        120 tets
        80  tricues (J3)
        20  trips

related: ..Fox 2 ..ofx 3 ..xxo 5 ..xof &#zx
  = ..oxfxo.. 3 ..xoxox.. 5 ..xfofx.. &#xt
  → CRF with cell list:
        30 bilbiroes (J91)
        40 octs
        24 peroes (J6)
        2  tids
        60 tets
        20 trips
13:B23D1E3: BAFox 2 ooofx 3 xoxxo 5 ofxof &#zx
  = oooxfxooo 3 xoxoxoxox 5 ofxfofxfo &#xt
  → CRF with cell list:
        30  bilbiroes (J91)
        2   ids
        40  octs
        48  peroes (J6)
        140 tets
        20  trips

related: ..Fox 2 ..ofx 3 ..xxo 5 ..xof &#zx
  = ..oxfxo.. 3 ..xoxox.. 5 ..xfofx.. &#xt
  → CRF with cell list:
        30 bilbiroes (J91)
        40 octs
        24 peroes (J6)
        2  tids
        60 tets
        20 trips
14:C4D1: BAFox 2 oxofo 3 oofox 5 xxoxx &#zx
  = oxoofooxo 3 oofxoxfoo 5 xxoxxxoxx &#xt
  → CRF with cell list:
        2   does
        24  pips
        24  pocuroes (J32)
        120 squippies (J1)
        40  teddies (J63)
        40  tets
        140 trips

related: .AFox 2 .xofo 3 .ofox 5 .xoxx &#zx
  = .xoofoox. 3 .ofxoxfo. 5 .xoxxxox. &#xt
  → CRF with cell list:
        24  pocuroes (J32)
        120 squippies (J1)
        2   srids
        40  teddies (J63)
        80  trips

related: ...ox 2 ...fo 3 ...ox 5 ...xx &#zx
  = ...ofo... 3 ...xox... 5 ...xxx... &#xt
  → CRF with cell list:
        24 pecues (J5)
        60 squippies (J1)
        2  tids
        80 trips
24:B2C4: VFfxo 2 xoxFx 3 oxfox 5 xxoxx &#zx
  = xoxFxFxox 3 oxfoxofxo 5 xxoxxxoxx &#xt
  → CRF with cell list:
        40  octs
        12  pips
        24  pocuroes (J32)
        120 squippies (J1)
        2   srids
        120 tets
        40  thawroes (J92)
        180 trips

related: .Ffxo 2 .oxFx 3 .xfox 5 .xoxx &#zx
  = .oxFxFxo. 3 .xfoxofx. 5 .xoxxxox. &#xt
  → CRF with cell list:
        24  peroes (J6)
        12  pips
        120 squippies (J1)
        120 tets
        40  thawroes (J92)
        2   tids
        120 trips
34:C4E3: VFfxo 2 oxofx 3 xxFxo 5 xxoxF &#zx
  = oxofxfoxo 3 xxFxoxFxx 5 xxoxFxoxx &#xt
  → CRF with cell list:
        30  bilbiroes (J91)
        60  dips
        240 squippies (J1)
        40  thawroes (J92)
        2   tids
        40  tricues (J3)
        60  trips

related: .Ffxo 2 .xofx 3 .xFxo 5 .xoxF &#zx
  = .xofxfox. 3 .xFxoxFx. 5 .xoxFxox. &#xt
  → CRF with cell list:
        30  bilbiroes (J91)
        36  dips
        2   grids
        240 squippies (J1)
        40  thawroes (J92)
124:B2C4D1: BAFox 2 xoxFx 3 oxfox 5 xxoxx &#zx
  → ‡) (f in C)
in . o3o5o subsymmetry   (up)
additional,
not prismatically symmetric
combinations of formers:
3:(B23)E3:
oxo|fxf|ooo 3 xxx|xox|xox 5 oox|ofo|xfo &#xt
  → CRF with cell list:
        2   ids
        30  ikes
        40  octs
        36  pips
        12  pocuroes (J32)
        180 squippies (J1)
        130 tets
        40  tricues (J3)
        60  trips
13:(B23)D1E3:
oxo|xfx|ooo 3 xxx|oxo|xox 5 oox|fof|xfo &#xt
  → CRF with cell list:
        30  bilbiroes (J91)
        2   ids
        40  octs
        24  peroes (J6)
        12  pips
        12  pocuroes (J32)
        130 tets
        40  tricues (J3)
        20  trips
using here node marks / (pseudo) edge lengths: F=f+x, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x

in o3o3o3o subsymmetry   (up)
Representation:
xffoo 3 oxoof 3 fooxo 3 ooffx &#zx  (ex)
All layers &
kaleido-facetings per layer:
A:  x3o3f3o   →  A1: (-x)3  x 3  f 3  o   →  A12:  o 3(-x)3  F 3 o
B:  f3x3o3o   →  B2:   F 3(-x)3  x 3  o   →  B23:  F 3  o 3(-x)3 x   →  B234:   F 3 o 3 o 3(-x)
C:  f3o3o3f
D:  o3o3x3f   →  D3:   o 3  x 3(-x)3  F   →  D32:  x 3(-x)3  o 3 F   →  D321: (-x)3 o 3 o 3  F
E:  o3f3o3x   →  E4:   o 3  f 3  x 3(-x)  →  E43:  o 3  F 3(-x)3 o
A priori invalid combinations:
none
Other layer-combinations:
A1:             (-x)ffoo 3 xxoof 3 fooxo 3 ooffx &#zx
D321:           xff(-x)o 3 oxoof 3 foooo 3 oofFx &#zx  → †)
A1D321:         (-x)ff(-x)o 3 xxoof 3 foooo 3 oofFx &#zx  → †)
A12:            offoo 3 (-x)xoof 3 Fooxo 3 ooffx &#zx
B2:             xFfoo 3 o(-x)oof 3 fxoxo 3 ooffx &#zx
D32:            xffxo 3 oxo(-x)f 3 foooo 3 oofFx &#zx
A12B2:          oFfoo 3 (-x)(-x)oof 3 Fxoxo 3 ooffx &#zx
B2D32:          xFfxo 3 o(-x)o(-x)f 3 fxooo 3 oofFx &#zx
A12D32:         offxo 3 (-x)xo(-x)f 3 Foooo 3 oofFx &#zx  → †)
A12B2D32:       oFfxo 3 (-x)(-x)o(-x)f 3 Fxooo 3 oofFx &#zx  → †)
A1B2:           (-x)Ffoo 3 x(-x)oof 3 fxoxo 3 ooffx &#zx
A1D32:          (-x)ffxo 3 xxo(-x)f 3 foooo 3 oofFx &#zx
B2D321:         xFf(-x)o 3 o(-x)oof 3 fxooo 3 oofFx &#zx
A12D321:        off(-x)o 3 (-x)xoof 3 Foooo 3 oofFx &#zx  → †)
A1B2D32:        (-x)Ffxo 3 x(-x)o(-x)f 3 fxooo 3 oofFx &#zx
A1B2D321:       (-x)Ff(-x)o 3 x(-x)oof 3 fxooo 3 oofFx &#zx  → †)
A12B2D321:      oFf(-x)o 3 (-x)(-x)oof 3 Fxooo 3 oofFx &#zx  → †)
A1D3:           (-x)ffoo 3 xxoxf 3 foo(-x)o 3 oofFx &#zx
A1B23:          (-x)Ffoo 3 xooof 3 f(-x)oxo 3 oxffx &#zx
A1E43:          (-x)ffoo 3 xxooF 3 foox(-x) 3 ooffo &#zx
B23D321:        xFf(-x)o 3 oooof 3 f(-x)ooo 3 oxfFx &#zx  → †)
D321E43:        xff(-x)o 3 oxooF 3 fooo(-x) 3 oofFo &#zx  → †)
A1B23D3:        (-x)Ffoo 3 xooxf 3 f(-x)o(-x)o 3 oxfFx &#zx
A1D3E43:        (-x)ffoo 3 xxoxF 3 foo(-x)(-x) 3 oofFo &#zx  → †)
A1B23D321:      (-x)Ff(-x)o 3 xooof 3 f(-x)ooo 3 oxfFx &#zx  → †)
A1B23E43:       (-x)Ffoo 3 xoooF 3 f(-x)ox(-x) 3 oxffo &#zx  → †)
A1D321E43:      (-x)ff(-x)o 3 xxooF 3 fooo(-x) 3 oofFo &#zx  → †)
B23D321E43:     xFf(-x)o 3 ooooF 3 f(-x)oo(-x) 3 oxfFo &#zx  → †)
A1B23D3E43:     (-x)Ffoo 3 xooxF 3 f(-x)o(-x)(-x) 3 oxfFo &#zx  → †)
A1B23D321E43:   (-x)Ff(-x)o 3 xoooF 3 f(-x)oo(-x) 3 oxfFo &#zx  → †)
A1E4:           (-x)ffoo 3 xxoof 3 fooxx 3 ooff(-x) &#zx
A1B234:         (-x)Ffoo 3 xooof 3 fooxo 3 o(-x)ffx &#zx  → †)
B234D321:       xFf(-x)o 3 oooof 3 foooo 3 o(-x)fFx &#zx  → †)
A1B234D321:     (-x)Ff(-x)o 3 xooof 3 foooo 3 o(-x)fFx &#zx  → †)
A1B234E4:       (-x)Ffoo 3 xooof 3 fooxx 3 o(-x)ff(-x) &#zx  → †)
A1B234D321E4:   (-x)Ff(-x)o 3 xooof 3 fooox 3 o(-x)fF(-x) &#zx  → †)
B2D3:           xFfoo 3 o(-x)oxf 3 fxo(-x)o 3 oofFx &#zx
A12D3:          offoo 3 (-x)xoxf 3 Foo(-x)o 3 oofFx &#zx  → †)
A12B23:         oFfoo 3 (-x)ooof 3 F(-x)oxo 3 oxffx &#zx
A12E43:         offoo 3 (-x)xooF 3 Foox(-x) 3 ooffo &#zx
B23D32:         xFfxo 3 ooo(-x)f 3 f(-x)ooo 3 oxfFx &#zx
A12B2D3:        oFfoo 3 (-x)(-x)oxf 3 Fxo(-x)o 3 oofFx &#zx  → †)
A12B23D3:       oFfoo 3 (-x)ooxf 3 F(-x)o(-x)o 3 oxfFx &#zx  → †)
A12B2E43:       oFfoo 3 (-x)(-x)ooF 3 Fxox(-x) 3 ooffo &#zx  → †)
A12B23D32:      oFfxo 3 (-x)oo(-x)f 3 F(-x)ooo 3 oxfFx &#zx  → †)
A12B2E43:       oFfoo 3 (-x)(-x)ooF 3 Fxox(-x) 3 ooffo &#zx  → †)
A12B23E43:      oFfoo 3 (-x)oooF 3 F(-x)ox(-x) 3 oxffo &#zx  → †)
A12B2D3E43:     oFfoo 3 (-x)(-x)oxF 3 Fxo(-x)(-x) 3 oofFo &#zx  → †)
A12B23D3E43:    oFfoo 3 (-x)ooxF 3 F(-x)o(-x)(-x) 3 oxfFo &#zx  → †)
A12B23D32E43:   oFfxo 3 (-x)oo(-x)F 3 F(-x)oo(-x) 3 oxfFo &#zx  → †)
A1B2D3:         (-x)Ffoo 3 x(-x)oxf 3 fxo(-x)o 3 oofFx &#zx
A1B23D32:       (-x)Ffxo 3 xoo(-x)f 3 f(-x)ooo 3 oxfFx &#zx
A1B2E43:        (-x)Ffoo 3 x(-x)ooF 3 fxox(-x) 3 ooffo &#zx  → †)
A1D32E43:       (-x)ffxo 3 xxo(-x)F 3 fooo(-x) 3 oofFo &#zx  → †)
A12B23D321:     oFf(-x)o 3 (-x)ooof 3 F(-x)ooo 3 oxfFx &#zx  → †)
A12D321E43:     off(-x)o 3 (-x)xooF 3 Fooo(-x) 3 oofFo &#zx  → †)
B2D321E43:      xFf(-x)o 3 o(-x)ooF 3 fxoo(-x) 3 oofFo &#zx  → †)
A1B2D3E43:      (-x)Ffoo 3 x(-x)oxF 3 fxo(-x)(-x) 3 oofFo &#zx  → †)
A1B2D32E43:     (-x)Ffxo 3 x(-x)o(-x)F 3 fxoo(-x) 3 oofFo &#zx  → †)
A1B2D321E43:    (-x)Ff(-x)o 3 x(-x)ooF 3 fxoo(-x) 3 oofFo &#zx  → †)
A1B23D32E43:    (-x)Ffxo 3 xoo(-x)F 3 f(-x)oo(-x) 3 oxfFo &#zx  → †)
A12B2D321E43:   oFf(-x)o 3 (-x)(-x)ooF 3 Fxoo(-x) 3 oofFo &#zx  → †)
A12B23D321E43:  oFf(-x)o 3 (-x)oooF 3 F(-x)oo(-x) 3 oxfFo &#zx  → †)
A1B2E4:         (-x)Ffoo 3 x(-x)oof 3 fxoxx 3 ooff(-x) &#zx
A1B234D32:      (-x)Ffxo 3 xoo(-x)f 3 foooo 3 o(-x)fFx &#zx  → †)
A1D32E4:        (-x)ffxo 3 xxo(-x)f 3 fooox 3 oofF(-x) &#zx
B2D321E4:       xFf(-x)o 3 o(-x)oof 3 fxoox 3 oofF(-x) &#zx  → †)
A12B234D321:    oFf(-x)o 3 (-x)ooof 3 Foooo 3 o(-x)fFx &#zx  → †)
A12D321E4:      off(-x)o 3 (-x)xoof 3 Fooox 3 oofF(-x) &#zx  → †)
A1B2D32E4:      (-x)Ffxo 3 x(-x)o(-x)f 3 fxoox 3 oofF(-x) &#zx  → †)
A1B2D321E4:     (-x)Ff(-x)o 3 x(-x)oof 3 fxoox 3 oofF(-x) &#zx  → †)
A12B2D321E4     oFf(-x)o 3 (-x)(-x)oof 3 Fxoox 3 oofF(-x) &#zx  → †)
A1B234D32E4:    (-x)Ffxo 3 xoo(-x)f 3 fooox 3 o(-x)fF(-x) &#zx  → †)
A12B234D321E4:  oFf(-x)o 3 (-x)ooof 3 Fooox 3 o(-x)fF(-x) &#zx  → †)
A1B2D3E4:       (-x)Ffoo 3 x(-x)oxf 3 fxo(-x)x 3 oofF(-x) &#zx  → †)
A1B23D32E4:     (-x)Ffxo 3 xoo(-x)f 3 f(-x)oox 3 oxfF(-x) &#zx  → †)
A1B234D32E43:   (-x)Ffxo 3 xoo(-x)F 3 fooo(-x) 3 o(-x)fFo &#zx  → †)
A12B234D321E43: oFf(-x)o 3 (-x)oooF 3 Fooo(-x) 3 o(-x)fFo &#zx  → †)
Stott expansion:
(derived potential CRFs)
1:A1: oFFxx 3 xxoof 3 fooxo 3 ooffx &#zx
  → CRF with cell list:
        5   coes
        30  ikes
        20  octs
        90  squippies (J1)
        125 tets
        40  trips

related: oF.xx 3 xx.of 3 fo.xo 3 oo.fx &#zx
  → CRF with cell list:
        5  coes
        30 mibdies (J62)
        20 octs
        90 squippies (J1)
        20 teddies (J63)
        25 tets
        40 trips
2:A12: offoo 3 ouxxF 3 Fooxo 3 ooffx &#zx
  → ‡) (u in B)
2:B2: xFfoo 3 xoxxF 3 fxoxo 3 ooffx &#zx
  → CRF with cell list:
        20  ikes
        25  octs
        60  squippies (J1)
        270 tets
        40  tricues (J3)
        60  trips
        5   tuts
2:D32: xffxo 3 oxo(-x)f 3 foooo 3 oofFx &#zx
  → ‡) (u in B)
2:A12B2: oFfoo 3 ooxxF 3 Fxoxo 3 ooffx &#zx
  → CRF with cell list:
        30 bilbiroes (J91)
        25 octs
        20 teddies (J63)
        80 tets
        20 tricues (J3)
        5  tuts
12:A12B2: xAFxx 3 ooxxF 3 Fxoxo 3 ooffx &#zx
  → CRF with cell list:
        30 bilbiroes (J91)
        25 octs
        30 pips
        20 teddies (J63)
        60 tets
        5  toes
        40 tricues (J3)
        40 trips
2:B2D32: xFfxo 3 xoxoF 3 fxooo 3 oofFx &#zx
  → CRF with cell list:
        20 ikes
        25 octs
        60 squippies (J1)
        55 tets
        20 thawroes (J92)
12:A1B2: oAFxx 3 uoxxF 3 fxoxo 3 ooffx &#zx
  → ‡) (u in A)
12:A1D32: oFFux 3 uuxoF 3 foooo 3 oofFx &#zx
  → ‡) (u in A, u in B, u in D)
12: B2D321: uAFox 3 xoxxF 3 fxooo 3 oofFx &#zx
  → ‡) (u in A)
12:A1B2D32: oAFux 3 uoxoF 3 fxooo 3 oofFx &#zx
  → ‡) (u in A, u in D)
13:A1D3: oFFxx 3 xxoxf 3 Fxxox 3 oofFx &#zx
  → CRF with cell list:
        10 hips
        20 octs
        30 mibdies (J62)
        90 squippies (J1)
        20 thawroes (J92)
        40 tricues (J3)
        90 trips
        10 tuts
13:A1B23: oAFxx 3 xooof 3 Foxux 3 oxffx &#zx
  → ‡) (u in D)
13:A1E43: oFFxx 3 xxooF 3 Fxxuo 3 ooffo &#zx
  → ‡) (u in D)
13:A1B23D3: oAFxx 3 xooxf 3 Foxox 3 oxfFx &#zx
  → ‡) (f in C)
14:A1E4: oFFxx 3 xxoof 3 fooxx 3 xxFFo &#zx
  → CRF with cell list:
        60 bilbiroes (J91)
        10 coes
        40 octs
        70 tets
        20 trips
23:A12E43: offoo 3 ouxxA 3 Axxuo 3 ooffo &#zx
  → ‡) (u in B, u in D)
23:B2D3: xFfoo 3 xoxuF 3 Fuxox 3 oofFx &#zx
  → ‡) (u in B, u in D)
23:A12B23: oFfoo 3 oxxxF 3 Aoxux 3 oxffx &#zx
  → ‡) (u in D)
23:B23D32: xFfxo 3 xxxoF 3 Foxxx 3 oxfFx &#zx
  → CRF with cell list:
        10 coes
        60 pips
        30 tets
        40 thawroes (J92)
        40 tricues (J3)
123:A1B2D3: oAFxx 3 uoxuF 3 Fuxox 3 oofFx &#zx
  → ‡) (u in A, u in B, u in D)
123:A1B23D32: oAFux 3 uxxoF 3 Foxxx 3 oxfFx &#zx
  → ‡) (u in A, u in D)
124:A1B2E4: oAFxx 3 uoxxF 3 fxoxx 3 xxFFo &#zx
  → ‡) (u in A)
124:A1D32E4: oFFux 3 uuxoF 3 fooox 3 xxFAo &#zx
  → ‡) (u in A, u in B, u in D)
using here node marks / (pseudo) edge lengths: F=f+x, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x

in o3o3o *b3o subsymmetry   (up)
Representation:
foxo 3 ooof 3 xfoo *b3 oxfo &#zx  (ex)

with cyclical layer symmetry: A(134) → B(341) → C(413) → A(134)
All layers &
kaleido-facetings per layer:
A:  f3o3x *b3o  →  A1:   f 3 x 3(-x)*b3  o   →  A12:  F 3(-x)3 o *b3  x  →  A123:   F 3 o 3  o *b3(-x)
B:  o3o3f *b3x  →  B1:   o 3 x 3  f *b3(-x)  →  B12:  x 3(-x)3 F *b3  o  →  B123: (-x)3 o 3  F *b3  o
C:  x3o3o *b3f  →  C1: (-x)3 x 3  o *b3  f   →  C12:  o 3(-x)3 x *b3  F  →  C123:   o 3 o 3(-x)*b3  F
D:  o3f3o *b3o
A priori invalid combinations:
none
Other layer-combinations:
C1:           fo(-x)o 3 ooxf 3 xfoo *b3 oxfo &#zx
B123:         f(-x)xo 3 ooof 3 xFoo *b3 oofo &#zx  → †)
B123C1:       f(-x)(-x)o 3 ooxf 3 xFoo *b3 oofo &#zx  → †)
A12:          Foxo 3 (-x)oof 3 ofoo *b3 xxfo &#zx
A12B12:       Fxxo 3 (-x)(-x)of 3 oFoo *b3 xofo &#zx  → †)
A12B12C12:    Fxoo 3 (-x)(-x)(-x)f 3 oFxo *b3 xoFo &#zx  → †)
A12C1:        Fo(-x)o 3 (-x)oxf 3 ofoo *b3 xxfo &#zx  → †)
A12B123:      F(-x)xo 3 (-x)oof 3 oFoo *b3 xofo &#zx  → †)
A12B12C1:     Fx(-x)o 3 (-x)(-x)xf 3 oFoo *b3 xofo &#zx  → †)
A12B123C1:    F(-x)(-x)o 3 (-x)oxf 3 oFoo *b3 xofo &#zx  → †)
A1C1:         fo(-x)o 3 xoxf 3 (-x)foo *b3 oxfo &#zx
A1B123:       f(-x)xo 3 xoof 3 (-x)Foo *b3 oofo &#zx  → †)
B123C123:     f(-x)oo 3 ooof 3 xF(-x)o *b3 ooFo &#zx  → †)
A1B123C1:     f(-x)(-x)o 3 xoxf 3 (-x)Foo *b3 oofo &#zx  → †)
A1B123C123:   f(-x)oo 3 xoof 3 (-x)F(-x)o *b3 ooFo &#zx  → †)
A1B12C1:      fx(-x)o 3 x(-x)xf 3 (-x)Foo *b3 oofo &#zx  → †)
A1B123C12:    f(-x)oo 3 xo(-x)f 3 (-x)Fxo *b3 ooFo &#zx  → †)
A12B123C123:  F(-x)oo 3 (-x)oof 3 oF(-x)o *b3 xoFo &#zx  → †)
A1B1C1:       fo(-x)o 3 xxxf 3 (-x)foo *b3 o(-x)fo &#zx
A123B123C123: F(-x)oo 3 ooof 3 oF(-x)o *b3 (-x)oFo &#zx  → †)
Stott expansion:
(derived potential CRFs)
2:0: foxo 3 xxxF 3 xfoo *b3 oxfo &#zx
  → CRF with cell list:
        480 tets
        96  tricues (J3)
        96  trips
        24  tuts

related: fox. 3 xxx. 3 xfo. *b3 oxf. &#zx (prissi)
  → CRF with cell list:
        24 ikes
        96 tricues (J3)
        96 trips
        24 tuts
1:C1: Fxox 3 ooxf 3 xfoo *b3 oxfo &#zx
  → CRF with cell list:
        8   coes
        32  ikes
        40  octs
        96  squippies (J1)
        136 tets
        48  trips
2:A12: Foxo 3 oxxF 3 ofoo *b3 xxfo &#zx
  → CRF with cell list:
        136 tets
        32  thawroes (J92)
        32  tricues (J3)
        16  tuts
23:A12: Foxo 3 oxxF 3 xFxx *b3 xxfo &#zx
  → CRF with cell list:
        8  coes
        48 pips
        96 tets
        32 thawroes (J92)
        8  toes
        32 tricues (J3)
        48 trips
        8  tuts
13:A1C1: Fxox 3 xoxf 3 oFxx *b3 oxfo &#zx
  → CRF with cell list:
        8  coes
        40 octs
        96 squippies (J1)
        32 teddies (J63)
        32 thawroes (J92)
        96 trips
        8  tuts
134:A1B1C1: Fxox 3 xxxf 3 oFxx *b3 xoFx &#zx
  → ‡) (f in D)
using here node marks / (pseudo) edge lengths: F=f+x

in o5o2o5o subsymmetry   (up)
Representation:
xfooxo 5 xofxoo 2 oxofox 5 ooxofx &#zx  (ex)

with layer symmetry:
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234) ↔ 
       A(2143),C(2143),B(2143),E(2143),D(2143),F(2143)
and cycle:
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234) →
       F(3421),D(3421),E(3421),C(3421),B(3421),A(3421) →
       A(2143),C(2143),B(2143),E(2143),D(2143),F(2143) →
       F(4312),E(4312),D(4312),B(4312),C(4312),A(4312) →
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234)
All layers &
kaleido-facetings per layer:
A:  x5x o5o   →   A1: (-x)5  F   o 5  o    or    A2:   F 5(-x)  o 5  o
B:  f5o x5o   →   B3:   f 5  o (-x)5  f
C:  o5f o5x   →   C4:   o 5  f   f 5(-x)
D:  o5x f5o   →   D2:   f 5(-x)  f 5  o
E:  x5o o5f   →   E1: (-x)5  f   o 5  f
F:  o5o x5x   →   F3:   o 5  o (-x)5  F    or    F4:   o 5  o   F 5(-x)
A priori invalid combinations:
when component 1 (o5o2.5.) remains unchanged (neither A1, A2, D2, E1):
  B3 + neither F3 nor F4  → ‡) (u in F)
  C4 + neither F3 nor F4  → ‡) (u in F)
  F3 + no B3              → ‡) (u in B)
  F4 + no C4              → ‡) (u in C)

when component 2 (.5.2o5o) remains unchanged (neither B3, C4, F3, F4):
  E1 + neither A1 nor A2  → ‡) (u in A)
  D2 + neither A1 nor A2  → ‡) (u in A)
  A1 + no E1              → ‡) (u in E)
  A2 + no D2              → ‡) (u in D)

As changes in (o5o2.5.) do not affect (.5.2o5o) and vice versa,
the above exclusions become valid generally.
Other layer-combinations:
A1E1:         (-x)foo(-x)o 5 Fofxfo 2 oxofox 5 ooxofx &#zx
A1D2E1:       (-x)fof(-x)o 5 Fof(-x)fo 2 oxofox 5 ooxofx &#zx
A1B3E1F3:     (-x)foo(-x)o 5 Fofxfo 2 o(-x)ofo(-x) 5 ofxofF &#zx
A1B3D2E1F3:   (-x)fof(-x)o 5 Fof(-x)fo 2 o(-x)ofo(-x) 5 ofxofF &#zx  → †)
A2B3D2E1F3:   Ffof(-x)o 5 (-x)of(-x)fo 2 o(-x)ofo(-x) 5 ofxofF &#zx  → †)
A1B3C4D2E1F3: (-x)fof(-x)o 5 Fof(-x)fo 2 o(-x)ffo(-x) 5 of(-x)ofF &#zx  → †)
Stott expansion:
(derived potential CRFs)
1:A1E1: oFxxox 5 Fofxfo 2 oxofox 5 ooxofx &#zx
  → CRF with cell list:
        10  gyepips (J11)
        25  ikes
        10  pips
        150 squippies (J1)
        75  tets
        50  trips

related: .Fxxox 5 .ofxfo 2 .xofox 5 .oxofx &#zx
  → CRF with cell list:
        10  paps
        15  pips
        25  ikes
        75  tets
        50  trips
        125 squippies (J1)

related: oFxx.x 5 Fofx.o 2 oxof.x 5 ooxo.x &#zx
  → CRF with cell list:
        10 gyepips (J11)
        25 mibdies (J62)
        35 pips
        25 squippies (J1)
        75 tets
        50 trips

related: .Fxx.x 5 .ofx.o 2 .xof.x 5 .oxo.x &#zx
  → CRF with cell list:
        25 mibdies (J62)
        10 paps
        40 pips
        75 tets
        50 trips
12:A1D2E1: oFxFox 5 AxFoFx 2 oxofox 5 ooxofx &#zx
  → CRF with cell list:
        50 bilbiroes (J91)
        10 dips
        10 gyepips (J11)
        5  pips
        75 squippies (J1)
13:A1B3E1F3: oFxxox 5 Fofxfo 2 xoxFxo 5 ofxofF &#zx
  → ‡) (f in B)

using here node marks / (pseudo) edge lengths: F=f+x, A=F+x=f+2x

in o3o2o3o subsymmetry   (up)
Representation:
fFoxffooxo 3 foFfxofxoo 2 oxofofxFof 3 ooxofxfoFf &#zx  (ex)

with layer symmetry:
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234),G(1234),H(1234),I(1234),J(1234) ↔ 
       A(2143),C(2143),B(2143),E(2143),D(2143),G(2143),F(2143),I(2143),H(2143),J(2143)
and cycle:
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234),G(1234),H(1234),I(1234),J(1234) →
       J(3421),H(3421),I(3421),G(3421),F(3421),D(3421),E(3421),C(3421),B(3421),A(3421) →
       A(2143),C(2143),B(2143),E(2143),D(2143),G(2143),F(2143),I(2143),H(2143),J(2143) →
       J(4312),I(4312),H(4312),F(4312),G(4312),E(4312),D(4312),B(4312),C(4312),A(4312) →
       A(1234),B(1234),C(1234),D(1234),E(1234),F(1234),G(1234),H(1234),I(1234),J(1234)
All layers &
kaleido-facetings per layer:
A:  f3f o3o
B:  F3o x3o   →   B3:   F 3  o (-x)3  x   →   B34:   F 3  o   o 3(-x)
C:  o3F o3x   →   C4:   o 3  F   x 3(-x)  →   C43:   o 3  F (-x)3  o
D:  x3f f3o   →   D1: (-x)3  F   f 3  o
E:  f3x o3f   →   E2:   F 3(-x)  o 3  f
F:  f3o f3x   →   F4:   f 3  o   F 3(-x)
G:  o3f x3f   →   G3:   o 3  f (-x)3  F
H:  o3x F3o   →   H2:   x 3(-x)  F 3  o   →   H21: (-x)3  o   F 3  o
I:  x3o o3F   →   I1: (-x)3  x   o 3  F   →   I12:   o 3(-x)  o 3  F
J:  o3o f3f
A priori invalid combinations:
when component 1 (o3o2.3.) remains unchanged (neither D1, E2, H2, H21, I1, I12):
  B3 + C4                   → ‡) (u in B, u in C)
  B3 + F4                   → ‡) (u in B)
  B3 + no G3                → ‡) (u in G)
  B34 + neither C4 nor C43  → ‡) (u in C)
  B34 + no F4               → ‡) (u in F)
  C4 + no F4                → ‡) (u in F)
  C4 + G3                   → ‡) (u in C)
  C43 + neither B3 nor B34  → ‡) (u in B)
  C43 + no G3               → ‡) (u in G)
  F4 + neither C4 nor C43   → ‡) (u in C)
  G3 + neither B3 nor B34   → ‡) (u in B)

when component 2 (.3.2o3o) remains unchanged (neither B3, B34, C4, C43, F4, G3):
  D1 + H2                   → ‡) (u in H)
  D1 + neither I1 nor I12   → ‡) (u in I)
  E2 + neither H2 nor H21   → ‡) (u in H)
  E2 + I1                   → ‡) (u in I)
  H2 + no E2                → ‡) (u in E)
  H2 + I1                   → ‡) (u in H, u in I)
  H21 + no D1               → ‡) (u in D)
  H21 + neither I1 nor I12  → ‡) (u in I)
  I1 + no D1                → ‡) (u in D)
  I12 + no E2               → ‡) (u in E)
  I12 + neither H2 nor H21  → ‡) (u in H)

As changes in (o3o2.3.) do not affect (.3.2o3o) and vice versa,
the above exclusions become valid generally.
Other layer-combinations:
D1I1:                 fFo(-x)ffoo(-x)o 3 foFFxofxxo 2 oxofofxFof 3 ooxofxfoFf &#zx
D1H21I1:              fFo(-x)ffo(-x)(-x)o 3 foFFxofoxo 2 oxofofxFof 3 ooxofxfoFf &#zx
D1E2H21I12:           fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 oxofofxFof 3 ooxofxfoFf &#zx
B3D1G3I1:             fFo(-x)ffoo(-x)o 3 foFFxofxxo 2 o(-x)ofof(-x)Fof 3 oxxofxFoFf &#zx
B3C43D1G3I1:          fFo(-x)ffoo(-x)o 3 foFFxofxxo 2 o(-x)(-x)fof(-x)Fof 3 oxoofxFoFf &#zx
B3D1G3H21I1:          fFo(-x)ffo(-x)(-x)o 3 foFFxofoxo 2 o(-x)ofof(-x)Fof 3 oxxofxFoFf &#zx
B3C43D1G3H21I1:       fFo(-x)ffo(-x)(-x)o 3 foFFxofoxo 2 o(-x)(-x)fof(-x)Fof 3 oxoofxFoFf &#zx  → †)
B3D1E2G3H21I12:       fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 o(-x)ofof(-x)Fof 3 oxxofxFoFf &#zx
B3C43D1E2G3H21I12:    fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 o(-x)(-x)fof(-x)Fof 3 oxoofxFoFf &#zx  → †)
B34C43D1E2F4G3H21I12: fFo(-x)Ffo(-x)oo 3 foFF(-x)ofo(-x)o 2 oo(-x)foF(-x)Fof 3 o(-x)oof(-x)FoFf &#zx  → †)
Stott expansion:
(derived potential CRFs)
1:D1I1: FAxoFFxxox 3 foFFxofxxo 2 oxofofxFof 3 ooxofxfoFf &#zx
  → CRF with cell list:
        27  ikes
        6   octs
        72  squippies (J1)
        138 tets
        6   tricues (J3)
        30  trips
1:D1H21I1: FAxoFFxoox 3 foFFxofoxo 2 oxofofxFof 3 ooxofxfoFf &#zx
  → CRF with cell list:
        9  bilbiroes (J91)
        18 gyepips (J11)
        9  ikes
        54 squippies (J1)
        87 tets
        12 trips
12:D1E2H21I12: FAxoAFxoxx 3 FxAAoxFxox 2 oxofofxFof 3 ooxofxfoFf &#zx
  → CRF with cell list:
        18 bilbiroes (J91)
        18 pips
        54 squippies (J1)
        36 teddies (J63)
        12 tets
        12 tricues (J3)
        24 trips
13:B3D1G3I1: FAxoFFxxox 3 foFFxofxxo 2 xoxFxFoAxF 3 oxxofxFoFf &#zx
  → CRF with cell list:
        27 bilbiroes (J91)
        3  hips
        12 octs
        9  mibdies (J62)
        54 squippies (J1)
        18 teddies (J63)
        36 tets
        12 tricues (J3)
        30 trips
13:B3C43D1G3I1: FAxoFFxxox 3 foFFxofxxo 2 xooFxFoAxF 3 oxoofxFoFf &#zx
  → †) (dead end at D)
13:B3D1G3H21I1: FAxoFFxoox 3 foFFxofoxo 2 xoxFxFoAxF 3 oxxofxFoFf &#xz
  → †) (dead end at D)
123:B3D1E2G3H21I12: FAxoAFxoxx 3 FxAAoxFxox 2 xoxFxFoAxF 3 oxxofxFoFf &#zx
  → †) (dead end at D)


using here node marks / (pseudo) edge lengths: F=f+x, A=F+x=f+2x

in . o3o3o subsymmetry   (up)
Representation:
xoo|fox|Ffo|ofx|ofo 3 oof|oxf|ooo|fxo|foo 3 ofo|xfo|ofF|xof|oox &#xt  (ex)
All layers &
kaleido-facetings per layer:
A:  x3o3o  →  A1: (-x)3  x 3  o   →  A12:   o 3(-x)3 x  →  A123:  o 3 o 3(-x)
B:  o3o3f
C:  o3f3o
D:  f3o3x  →  D3:   f 3  x 3(-x)  →  D32:   F 3(-x)3 o
E:  o3x3f  →  E2:   x 3(-x)3  F   →  E21: (-x)3  o 3 F
F:  x3f3o  →  F1: (-x)3  F 3  o
G:  F3o3o
H:  f3o3f
g:  o3o3F
f:  o3f3x  →  f3:   o 3  F 3(-x)
etc. antisymmetrically
A priori invalid combinations:
A1 + D32                      → ‡) (u in A)
A1 + E2                       → ‡) (u in A, u in E)
A1 + no F1                    → ‡) (u in F)
A1 + e2                       → ‡) (u in A)
A1 + d12                      → ‡) (u in A)
A1 + neither d1 nor d12       → ‡) (u in d)
A1 + a32                      → ‡) (u in A, u in a)
A12 + D3                      → ‡) (u in A, u in D)
A12 + d1                      → ‡) (u in A, u in d)
A12 + neither E2 nor E21      → ‡) (u in E)
A12 + f3                      → ‡) (u in A)
A12 + e23                     → ‡) (u in A)
A12 + neither e2 nor e23      → ‡) (u in e)
A12 + a3                      → ‡) (u in A, u in a)
A123 + neither D3 nor D32     → ‡) (u in D)
A123 + no f3                  → ‡) (u in f)
A123 + e2                     → ‡) (u in e)
A123 + neither a3, a32, a321  → ‡) (u in a)
D3 + E2                       → ‡) (u in D)
D3 + no f3                    → ‡) (u in f)
D3 + e2                       → ‡) (u in D, u in e)
D3 + d12                      → ‡) (u in D)
D3 + a32                      → ‡) (u in D, u in a)
D3 + neither a3, a32, a321    → ‡) (u in a)
D32 + neither E2 nor E21      → ‡) (u in E)
D32 + neither e2 nor e23      → ‡) (u in e)
D32 + d1                      → ‡) (u in d)
D32 + a3                      → ‡) (u in a)
E2 + F1                       → ‡) (u in E)
E2 + neither e2 nor e23       → ‡) (u in e)
E2 + d1                       → ‡) (u in E, u in d)
E2 + a3                       → ‡) (u in E)
E2 + a321                     → ‡) (u in E)
E21 + neither A1, A12, A123   → ‡) (u in A)
E21 + no F1                   → ‡) (u in F)
E21 + neither d1 nor d12      → ‡) (u in d)
E21 + a32                     → ‡) (u in a)
F1 + neither A1, A12, A123    → ‡) (u in A)
F1 + neither d1 nor d12       → ‡) (u in d)
F1 + a32                      → ‡) (u in a)
f3 + neither D3 nor D32       → ‡) (u in D)
f3 + e2                       → ‡) (u in e)
f3 + neither a3, a32, a321    → ‡) (u in a)
e2 + neither E2 nor E21       → ‡) (u in E)
e2 + d1                       → ‡) (u in d)
e2 + a3                       → ‡) (u in e, u in a)
e23 + neither D3 nor D32      → ‡) (u in D)
e23 + no f3                   → ‡) (u in f)
e23 + neither a3, a32, a321   → ‡) (u in a)
d1 + neither A1, A12, A123    → ‡) (u in A)
d1 + no F1                    → ‡) (u in F)
d1 + a32                      → ‡) (u in d, u in a)
d12 + neither E2 nor E21      → ‡) (u in E)
d12 + neither e2 nor e23      → ‡) (u in e)
d12 + a3                      → ‡) (u in a)
a3 + neither D3 nor D32       → ‡) (u in D)
a3 + no f3                    → ‡) (u in f)
a32 + neither E2 nor E21      → ‡) (u in E)
a32 + neither e2 nor e23      → ‡) (u in e)
a321 + neither A1, A12, A123  → ‡) (u in A)
a321 + no F1                  → ‡) (u in F)
a321 + neither d1 nor d12     → ‡) (u in d)
Other layer-combinations:
A1F1d1:                   (-x)oo|fo(-x)|Ffo|of(-x)|ofo 3 xof|oxF|ooo|fxx|foo 3 ofo|xfo|ofF|xof|oox &#xt
A1E21F1d1:                (-x)oo|f(-x)(-x)|Ffo|of(-x)|ofo 3 xof|ooF|ooo|fxx|foo 3 ofo|xFo|ofF|xof|oox &#xt
A1F1d1a321:               (-x)oo|fo(-x)|Ffo|of(-x)|of(-x) 3 xof|oxF|ooo|fxx|foo 3 ofo|xfo|ofF|xof|ooo &#xt  → †)
A1E21F1d1a321:            (-x)oo|f(-x)(-x)|Ffo|of(-x)|of(-x) 3 xof|ooF|ooo|fxx|foo 3 ofo|xFo|ofF|xof|ooo &#xt  → †)
E2e2:                     xoo|fxx|Ffo|oFx|ofo 3 oof|o(-x)f|ooo|f(-x)o|foo 3 ofo|xFo|ofF|xxf|oox &#xt
A12E2e2:                  ooo|fxx|Ffo|oFx|ofo 3 (-x)of|o(-x)f|ooo|f(-x)o|foo 3 xfo|xFo|ofF|xxf|oox &#xt
D32E2e2:                  xoo|Fxx|Ffo|oFx|ofo 3 oof|(-x)(-x)f|ooo|f(-x)o|foo 3 ofo|oFo|ofF|xxf|oox &#xt
A12D32E2e2:               ooo|Fxx|Ffo|oFx|ofo 3 (-x)of|(-x)(-x)f|ooo|f(-x)o|foo 3 xfo|oFo|ofF|xxf|oox &#xt  → †) (dead end at D)
A12E2e2d12:               ooo|fxx|Ffo|oFo|ofo 3 (-x)of|o(-x)f|ooo|f(-x)(-x)|foo 3 xfo|xFo|ofF|xxF|oox &#xt
A12E2e2a32:               ooo|fxx|Ffo|oFx|ofx 3 (-x)of|o(-x)f|ooo|f(-x)o|fo(-x) 3 xfo|xFo|ofF|xxf|ooo &#xt
D32E2e2d12:               xoo|Fxx|Ffo|oFo|ofo 3 oof|(-x)(-x)f|ooo|f(-x)(-x)|foo 3 ofo|oFo|ofF|xxF|oox &#xt
A12D32E2e2d12:            ooo|Fxx|Ffo|oFo|ofo 3 (-x)of|(-x)(-x)f|ooo|f(-x)(-x)|foo 3 xfo|oFo|ofF|xxF|oox &#xt  → †) (dead end at D)
A12D32E2e2a32:            ooo|Fxx|Ffo|oFx|ofx 3 (-x)of|(-x)(-x)f|ooo|f(-x)o|fo(-x) 3 xfo|oFo|ofF|xxf|ooo &#xt  → †) (dead end at D)
A12D32E2e2d12a32:         ooo|Fxx|Ffo|oFo|ofx 3 (-x)of|(-x)(-x)f|ooo|f(-x)(-x)|fo(-x) 3 xfo|oFo|ofF|xxF|ooo &#xt  → †) (dead end at D)
A12E21F1e2d12:            ooo|f(-x)(-x)|Ffo|oFo|ofo 3 (-x)of|ooF|ooo|f(-x)(-x)|foo 3 xfo|xFo|ofF|xxF|oox &#xt
A12D32E21F1e2d12:         ooo|F(-x)(-x)|Ffo|oFo|ofo 3 (-x)of|(-x)oF|ooo|f(-x)(-x)|foo 3 xfo|oFo|ofF|xxF|oox &#xt  → †) (dead end at D)
A12E21F1e2d12a321:        ooo|f(-x)(-x)|Ffo|oFo|of(-x) 3 (-x)of|ooF|ooo|f(-x)(-x)|foo 3 xfo|xFo|ofF|xxF|ooo &#xt  → †)
A12D32E21F1e2d12a321:     ooo|F(-x)(-x)|Ffo|oFo|of(-x) 3 (-x)of|(-x)oF|ooo|f(-x)(-x)|foo 3 xfo|oFo|ofF|xxF|ooo &#xt  → †)
A1D3F1f3d1a3:             (-x)oo|fo(-x)|Ffo|of(-x)|ofo 3 xof|xxF|ooo|Fxx|fox 3 ofo|(-x)fo|ofF|(-x)of|oo(-x) &#xt
A1D3F1f3d1a321:           (-x)oo|fo(-x)|Ffo|of(-x)|of(-x) 3 xof|xxF|ooo|Fxx|foo 3 ofo|(-x)fo|ofF|(-x)of|ooo &#xt  → †)
A123D3F1f3d1a321:         ooo|fo(-x)|Ffo|of(-x)|of(-x) 3 oof|xxF|ooo|Fxx|foo 3 (-x)fo|(-x)fo|ofF|(-x)of|ooo &#xt  → †)
A1D3E21F1f3d1a3:          (-x)oo|f(-x)(-x)|Ffo|of(-x)|ofo 3 xof|xoF|ooo|Fxx|fox 3 ofo|(-x)Fo|ofF|(-x)of|oo(-x) &#xt
A1D3E21F1f3d1a321:        (-x)oo|f(-x)(-x)|Ffo|of(-x)|of(-x) 3 xof|xoF|ooo|Fxx|foo 3 ofo|(-x)Fo|ofF|(-x)of|ooo &#xt  → †)
A123D3E21F1f3d1a321:      ooo|f(-x)(-x)|Ffo|of(-x)|of(-x) 3 oof|xoF|ooo|Fxx|foo 3 (-x)fo|(-x)Fo|ofF|(-x)of|ooo &#xt  → †)
A1D3F1f3e23d1a321:        (-x)oo|fo(-x)|Ffo|oF(-x)|of(-x) 3 xof|xxF|ooo|Fox|foo 3 ofo|(-x)fo|ofF|(-x)(-x)f|ooo &#xt  → †)
A1D3E21F1f3e23d1a3:       (-x)oo|f(-x)(-x)|Ffo|oF(-x)|ofo 3 xof|xoF|ooo|Fox|fox 3 ofo|(-x)Fo|ofF|(-x)(-x)f|oo(-x) &#xt
A1D3E21F1f3e23d1a321:     (-x)oo|f(-x)(-x)|Ffo|oF(-x)|of(-x) 3 xof|xoF|ooo|Fox|foo 3 ofo|(-x)Fo|ofF|(-x)(-x)f|ooo &#xt  → †)
A123D3E21F1f3e23d1a321:   ooo|f(-x)(-x)|Ffo|oF(-x)|of(-x) 3 oof|xoF|ooo|Fox|foo 3 (-x)fo|(-x)Fo|ofF|(-x)(-x)f|ooo &#xt  → †)
A123D32E21F1f3e23d12a321: ooo|F(-x)(-x)|Ffo|oFo|of(-x) 3 oof|(-x)oF|ooo|Fo(-x)|foo 3 (-x)fo|oFo|ofF|(-x)(-x)F|ooo &#xt  → †)
Stott expansion:
(derived potential CRFs)
1:A1F1d1: oxxFxoAFxxFoxFx 3 xofoxFooofxxfoo 3 ofoxfoofFxofoox &#xt
  ...
1:A1E21F1d1: oxxFooAFxxFoxFx 3 xofooFooofxxfoo 3 ofoxFoofFxofoox &#xt
  ...
2:E2e2: xoofxxFfooFxofo 3 xxFxoFxxxFoxFxx 3 ofoxFoofFxxfoox &#xt
  → CRF with cell list:
        16  octs
        24  ikes
        72  squippies (J1)
        198 tets
        24  tricues (J3)
        48  trips
        2   tuts

related: xo.fxxFfooFx.fo 3 xx.xoFxxxFox.xx 3 of.xFoofFxxf.ox &#xt
  → CRF with cell list:
        24 gyepips (J11)
        12 mibdies (J62)
        16 octs
        72 squippies (J1)
        78 tets
        24 tricues (J3)
        48 trips
        2  tuts
2:A12E2|e2: ooofxx|Ffo|oFxofo 3 oxFxoF|xxx|FoxFxx 3 xfoxFo|ofF|xxfoox &#xt
  → CRF with cell list:
        24  ikes
        16  octs
        72  squippies (J1)
        155 tets
        4   thawroes (J92)
        16  tricues (J3)
        36  trips
        1   tut
(asymmetric hemiglomal combination of others)
2:D32E2|e2: xooFxx|Ffo|oFxofo 3 xxFooF|xxx|FoxFxx 3 ofooFo|ofF|xxfoox &#xt
  → CRF with cell list:
        12  bilbiroes (J91)
        12  ikes
        12  mibdies (J62)
        16  octs
        48  squippies (J1)
        122 tets
        16  tricues (J3)
        24  trips
        2   tuts
(asymmetric hemiglomal combination of others)
2:A12E2|e2d12: ooofxx|Ffo|oFoofo 3 oxFxoF|xxx|FooFxx 3 xfoxFo|ofF|xxFoox &#xt
  → CRF with cell list:
        12 bilbiroes (J91)
        12 ikes
        12 mibdies (J62)
        16 octs
        48 squippies (J1)
        79 tets
        4  thawroes (J92)
        8  tricues (J3)
        12 trips
        1  tut
(asymmetric hemiglomal combination of others)
2:A12E2e2a32: ooofxxFfooFxofx 3 oxFxoFxxxFoxFxo 3 xfoxFoofFxxfooo &#xt
  → CRF with cell list:
        24  ikes
        16  octs
        72  squippies (J1)
        112 tets
        8   thawroes (J92)
        8   tricues (J3)
        24  trips
2:D32E2e2d12: xooFxxFfooFoofo 3 xxFooFxxxFooFxx 3 ofooFoofFxxFoox &#xt
  → CRF with cell list:
        24 bilbiroes (J91)
        24 mibdies (J62)
        16 octs
        24 squippies (J1)
        46 tets
        8  tricues (J3)
        2  tuts
12:A12E21F1e2d12: xxxFooAFxxAxxFx 3 oxFxxAxxxFooFxx 3 xfoxFoofFxxFoox &#xt
  → CRF with cell list:
        24 bilbiroes (J91)
        1  co
        8  octs
        30 pips
        18 squippies (J1)
        24 teddies (J63)
        12 tets
        4  thawroes (J92)
        1  toe
        28 tricues (J3)
        24 trips
13:A1D3F1f3d1a3: oxxFxoAFxxFoxFx 3 xofxxFoooFxxfox 3 xFxoFxxFAoxFxxo &#xt
  → CRF with cell list:
        24 bilbiroes (J91)
        16 octs
        48 squippies (J1)
        24 teddies (J63)
        30 tets
        8  thawroes (J92)
        16 tricues (J3)
        48 trips
        2  tuts
13:A1D3E21F1f3d1a3: oxxFooAFxxFoxFx 3 xofxoFoooFxxfox 3 xFxoAxxFAoxFxxo &#xt
  ...
13:A1D3E21F1f3e23d1a3: oxxFooAFxxAoxFx 3 xofxoFoooFoxfox 3 xFxoAxxFAooFxxo &#xt
  ...
using here node marks / (pseudo) edge lengths: F=f+x, A=F+x=f+2x

in o2o2o2o subsymmetry   (up)
Representation:
ooo|xxx|fff|FFF|Vooo|f 2 Fxf|oFf|xFo|fxo|oVoo|f 2 xfF|Ffo|Fox|xof|ooVo|f 2 fFx|foF|oxF|ofx|oooV|f &#zx  (ex)
All layers &
kaleido-facetings per layer:
A:  o2F2x2f  →  A3:   o 2  F 2(-x)2  f
B:  o2x2f2F  →  B2:   o 2(-x)2  f 2  F
C:  o2f2F2x  →  C4:   o 2  f 2  F 2(-x)

D:  x2o2F2f  →  D1: (-x)2  o 2  F 2  f
E:  x2F2f2o  →  E1: (-x)2  F 2  f 2  o
F:  x2f2o2F  →  F1: (-x)2  f 2  o 2  F

G:  f2x2F2o  →  G2:   f 2(-x)2  F 2  o
H:  f2F2o2x  →  H4:   f 2  F 2  o 2(-x)
I:  f2o2x2F  →  I3:   f 2  o 2(-x)2  F
J:  F2f2x2o  →  J3:   F 2  f 2(-x)2  o
K:  F2x2o2f  →  K2:   F 2(-x)2  o 2  f
L:  F2o2f2x  →  L4:   F 2  o 2  f 2(-x)

M:  V2o2o2o
N:  o2V2o2o
O:  o2o2V2o
P:  o2o2o2V

Q:  f2f2f2f
A priori invalid combinations:
A  + I3,J3
A3 + I,J
B  + G2,K2
B2 + G,K
C  + H4,L4
C4 + H,L
D  + E1,F1
D1 + E,F
E  + F1
E1 + F
G  + K2
G2 + K
H  + L4
H4 + L
I  + J3
I3 + J	(all giving rise to u edges)
Other layer-combinations:
ABCD1E1F1GHIJKL:          ooo(-x)(-x)(-x)fffFFFVooof 2 FxfoFfxFofxooVoof 2 xfFFfoFoxxofooVof 2 fFxfoFoxFofxoooVf &#zx
ABC4D1E1F1GH4IJKL4:       ooo(-x)(-x)(-x)fffFFFVooof 2 FxfoFfxFofxooVoof 2 xfFFfoFoxxofooVof 2 fF(-x)foFo(-x)Fof(-x)oooVf &#zx
AB2C4D1E1F1G2H4IJK2L4:    ooo(-x)(-x)(-x)fffFFFVooof 2 F(-x)foFf(-x)Fof(-x)ooVoof 2 xfFFfoFoxxofooVof 2 fF(-x)foFo(-x)Fof(-x)oooVf &#zx
A3B2C4D1E1F1G2H4I3J3K2L4: ooo(-x)(-x)(-x)fffFFFVooof 2 F(-x)foFf(-x)Fof(-x)ooVoof 2 (-x)fFFfoFo(-x)(-x)ofooVof 2 fF(-x)foFo(-x)Fof(-x)oooVf &#zx  → †)
Stott expansion:
(derived potential CRFs)
1:ABCD1E1F1GHIJKL: xxxoooFFFAAABxxxF 2 FxfoFfxFofxooVoof 2 xfFFfoFoxxofooVof 2 fFxfoFoxFofxoooVf &#zx
  → CRF with cell list:
        24  ikes
        60  squippies (J1)
        180 tets
        20  trips
(as this is just an axial change, the orthogonal symmetry remains; 
 thus it also can be described as: BAFox 2 oxofo 3 oooox 5 ooxoo &#zx)

related: xxxoooFFF.......F 2 FxfoFfxFo.......f 2 xfFFfoFox.......f 2 fFxfoFoxF.......f &#zx
  → CRF with cell list:
        6  bilbiroes (J91)
        2  does
        24 mibdies (J62)
        36 squippies (J1)
        16 tets
        8  trips
14:ABC4D1E1F1GH4IJKL4: xxxoooFFFAAABxxxF 2 FxfoFfxFofxooVoof 2 xfFFfoFoxxofooVof 2 FAoFxAxoAxFoxxxBF &#zx
  → CRF with cell list:
        16 bilbiroes (J91)
        16 gyepips (J11)
        64 squippies (J1)
        16 teddies (J63)
        24 tets
        24 trips
124:AB2C4D1E1F1G2H4IJK2L4: xxxoooFFFAAABxxxF 2 AoFxAFoAxFoxxBxxF 2 xfFFfoFoxxofooVof 2 FAoFxAxoAxFoxxxBF &#zx  → °)
using here node marks / (pseudo) edge lengths: F=f+x=ff, V=2f, A=F+x=f+2x, B=V+x=2f+x=fff


EKF of the icositetrachoron (x3o4o3o)

©

in o3o3o4o subsymmetry   (up)
Representation:
qo 3 oo 3 oo 4 ox &#zx  (ico)
All layers &
kaleido-facetings per layer:
A: q3o3o4o
B: o3o3o4x  →  B4: o3o3q4(-x)
A priori invalid combinations:
none
Other layer-combinations:
B4:  qo 3 oo 3 oq 4 o(-x) &#zx
Stott expansion:
(derived potential CRFs)
1:-: wx 3 oo 3 oo 4 ox &#zx
  → CRF with cell list:
        24 esquidpies (J15)
        16 tets
        32 trips
2:-: qo 3 xx 3 oo 4 ox &#zx
  = Wythoffian x3o4o3x (spic) with cell list:
        48  octs
        192 trips
3:-: qo 3 oo 3 xx 4 ox &#zx
  → CRF with cell list:
        8  coes
        24 squobcues (J28)
        16 tets
        64 trips
4:B4: qo 3 oo 3 oq 4 xo &#zx
  = Wythoffian o3x4o3o (rico) with cell list:
        24 coes
        24 cubes
12:-: wx 3 xx 3 oo 4 ox &#zx
  → CRF with cell list:
        24  esquidpies (J15)
        32  hips
        8   octs
        160 trips
        16  tuts
13:-: wx 3 oo 3 xx 4 ox &#zx
  = Wythoffian x3o4x3o (srico) with cell list:
        24 coes
        24 sircoes
        96 trips
14:B4: wx 3 oo 3 oq 4 xo &#zx
  → °) (asks for non-regular hexagons: wx .. oq .. &#zx)
23:-: qo 3 xx 3 xx 4 ox &#zx
  → CRF with cell list:
        64  hips
        24  squobcues (J28)
        8   toes
        128 trips
        16  tuts
24:B4: qo 3 xx 3 oq 4 xo &#zx
  = Wythoffian x3o4x3o (srico) with cell list:
        24 coes
        24 sircoes
        96 trips
34:B4: qo 3 oo 3 xw 4 xo &#zx
  → °) (asks for non-regular hexagons: qo .. xw .. &#zx)
123:-: wx 3 xx 3 xx 4 ox &#zx
  = Wythoffian x3x4o3x (prico) with cell list:
        96 hips
        24 sircoes
        24 toes
        96 trips
124:B4: wx 3 xx 3 oq 4 xo &#zx
  → °) (asks for non-regular hexagons: wx .. oq .. &#zx)
134:B4: wx 3 oo 3 xw 4 xo &#zx
  = Wythoffian o3x4x3o (cont) with cell list:
        48 tics
234:B4: qo 3 xx 3 xw 4 xo &#zx
  → °) (asks for non-regular hexagons: qo .. xw .. &#zx)
1234:B4: wx 3 xx 3 xw 4 xo &#zx
  = Wythoffian x3x4x3o (grico) with cell list:
        24 gircoes
        24 tics
        96 trips



(As it will turn out, the set of resulting polychora in o2o3o4o resp. . o3o4o here is identical to those which turn up from the corresponding consideration of hex wrt. these subsymmetries.)

in o2o3o4o subsymmetry   (up)
Representation:
qo 2 xo 3 ox 4 oo &#zx  (ico)
All layers &
kaleido-facetings per layer:
A: q2x3o4o   →   A2:  q 2(-x)3  x 4 o   →   A23:  q 2  o 3(-x)4 q
B: o2o3x4o   →   B3:  o 2  x 3(-x)4 q   →   B32:  o 2(-x)3  o 4 q
A priori invalid combinations:
A23                       → ‡) (q or w in extremal layers, i.e. A)

B32 + neither A2 nor A23  → ‡) (u in A)
A2 + B3                   → ‡) (u in A, u in B)
Other layer-combinations:
A2:     qo 2 (-x)o 3 xx 4 oo &#zx
A2B32:  qo 2 (-x)(-x) 3 xo 4 oq &#zx
B3:     qo 2 xx 3 o(-x) 4 oq &#zx
Stott expansion:
(derived potential CRFs)
1:-: wx 2 xo 3 ox 4 oo &#zx (pexic)
  → CRF with cell list:
        6  esquidpies (J15)
        18 octs
        8  trips
2:A2: qo 2 ox 3 xx 4 oo &#zx
  → CRF with cell list:
        2  coes
        12 cubes
        16 tricues (J3)
2:A2B32: qo 2 oo 3 xo 4 oq &#zx
  = Wythoffian o3o3x4o (rit) with cell list:
        8  coes
        16 tets
3:B3: qo 2 xx 3 xo 4 oq &#zx (pabdirico)
  → CRF with cell list:
        6  coes
        12 cubes
        2  toes
        16 tricues (J3)
4:-: qo 2 xo 3 ox 4 xx &#zx (pacsrit)
  → CRF with cell list:
        16 octs
        2  sircoes
        6  squobcues (J28)
        24 trips
12:A2: wx 2 ox 3 xx 4 oo &#zx
  → CRF with cell list:
        2  coes
        18 cubes
        8  hips
        16 tricues (J3)
12:A2B32: wx 2 oo 3 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: wx .. .. oq &#zx)
13:B3: wx 2 xx 3 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: wx .. .. oq &#zx)
14:-: wx 2 xo 3 ox 4 xx &:#zx
  = Wythoffian o3x3o4x (srit) with cell list:
        16 octs
        8  sircoes
        32 trips
2(-3):A2: qo 2 ox 3 oo 4 oo &#zx
  = Wythoffian x3o3o4o (hex) with cell list:
        16 tets
24:A2: qo 2 ox 3 xx 4 xx &#zx
  → CRF with cell list:
        12 ops
        2  tics
        16 tricues (J3)
        24 trips
24:A2B32: qo 2 oo 3 xo 4 xw &#zx
  → °) (asks for non-regular hexagons: qo .. .. xw &#zx)
34:B3: qo 2 xx 3 xo 4 xw &#zx
  → °) (asks for non-regular hexagons: qo .. .. xw &#zx)
12(-3):A2: wx 2 ox 3 oo 4 oo &#zx (pex hex)
  → CRF with cell list:
        16 tets
        8  trips
124:A2: wx 2 ox 3 xx 4 xx &#zx
  → CRF with cell list:
        12 cubes
        8  hips
        18 ops
        2  tics
        16 tricues (J3)
        24 trips
124: A2B32: wx 2 oo 3 xo 4 xw &#zx
  = Wythoffian o3o3x4x (tat) with cell list:
        16 tets
        8  tics
134:B3: wx 2 xx 3 xo 4 xw &#zx (pabdiproh)
  → CRF with cell list:
        2  gircoes
        12 ops
        6  tics
        16 tricues (J3)
        8  trips
2(-3)4:A2: qo 2 ox 3 oo 4 xx &#zx (pacsid pith)
  → CRF with cell list:
        14 cubes
        16 tets
        24 trips
12(-3)4:A2: wx 2 ox 3 oo 4 xx &#zx
  = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips

in . o3o4o subsymmetry   (up)
additional,
not prismatically symmetric
combinations of formers:
none 

(As A23 already was ruled out a priori this would ask for a local A and A2 at the top resp. bottom layer. 
 But that combination would suffer again from producing an u=2x sized edge in A.)


in o3o3o *b3o subsymmetry   (up)
Representation:
qoo 3 ooo 3 oqo *b3 ooq &#zx  (ico)
All layers &
kaleido-facetings per layer:
A: q3o3o *b3o
B: o3o3q *b3o
C: o3o3o *b3q

(As this representation does not show up (true / x-) edges within the layers, those thus cannot be inverted either. 
Therefore at most pure partial Stott expansions wrt. this subsymmetry remain possible.)
Stott expansion:
(derived potential CRFs)
1:-: wxx 3 ooo 3 oqo *b3 ooq &#zx (poxic)
  → CRF with cell list:
        24 esquidpies (J15)
        16 tets
        32 trips

related: .xx 3 .oo 3 .qo *b3 .oq &#zx
   = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips
2:-: qoo 3 xxx 3 oqo *b3 ooq &#zx
  = Wythoffian x3o4o3x (spic) with cell list:
        48  octs
        192 trips

related: .oo 3 .xx 3 .qo *b3 .oq &#zx
   = Wythoffian o3x3o4x (srit) with cell list:
        16 octs
        8  sircoes
        32 trips
12:-: wxx 3 xxx 3 oqo *b3 ooq &#zx (owau prit)
  → CRF with cell list:
        24  esquidpies (J15)
        32  hips
        8   octs
        160 trips
        16  tuts

related: .xx 3 .xx 3 .qo *b3 .oq &#zx
   = Wythoffian x3x3o4x (prit) with cell list:
        24 cubes
        32 hips
        8  sircoes
        16 tuts
13:-: wxx 3 ooo 3 xwx *b3 ooq &#zx (pocsric)
  → CRF with cell list:
        8  coes
        24 squobcues (J28)
        16 tets
        64 trips

related: wx. 3 oo. 3 xw. *b3 oo. &#zx
   = Wythoffian x3o3x4x (tat) with cell list:
        16 tets
        8  tics
123:-: wxx 3 xxx 3 xwx *b3 ooq &#zx (poc prico)
  → CRF with cell list:
        64  hips
        24  squobcues (J28)
        8   toes
        128 trips
        16  tuts

related: wx. 3 xx. 3 xw. *b3 oo. &#zx
   = Wythoffian o3x3x4x (grit) with cell list:
        8  gircoes
        32 trips
        16 tuts
134:-: wxx 3 ooo 3 xwx *b3 xxw &#zx
  = Wythoffian x3o4x3o (srico) with cell list:
        24 coes
        24 sircoes
        96 trips

related: wx. 3 oo. 3 xw. *b3 xx. &#zx
   = Wythoffian x3o3x4x (proh) with cell list:
        16 coes
        24 ops
        8  tics
        32 trips
1234:-: wxx 3 xxx 3 xwx *b3 xxw &#zx
  = Wythoffian x3x4o3x (prico) with cell list:
        96 hips
        24 sircoes
        24 toes
        96 trips

related: .xx 3 .xx 3 .wx *b3 .xw &#zx
   = Wythoffian x3x3x4x (gidpith) with cell list:
        8  gircoes
        32 hips
        24 ops
        16 toes



in o4o2o4o subsymmetry   (up)
Representation:
oxo 4 ooq 2 oxo 4 qoo &#zx  (ico)
All layers &
kaleido-facetings per layer:
A: o4o o4q 
B: x4o x4o   →  B1: (-x)4q x4o   →  B13: (-x)4q (-x)4q
             ↳  B3: x4o (-x)4q   →  (B31 = B13)
C: o4q o4o
Stott expansion:
(derived potential CRFs)
1:B1: xox 4 oqq 2 oxo 4 qoo &#zx
  → ‡) (q in C)
2:-: oxo 4 xxw 2 oxo 4 qoo &#zx (bicyte ausodip)
  → CRF with cell list:
        4  esquidpies (J15)
        16 octs
        4  squobcues (J28)
        16 trips

related: .xo 4 .xw 2 .xo 4 .oo &#zx (cyte cubau sodip)
  → CRF with cell list:
        4  esquidpies (J15)
        4  ops
        16 squippies (J1)
12:B1: xox 4 xww 2 oxo 4 qoo &#zx
  → ‡) (w in C)
13:B13: xox 4 oqq 2 xox 4 qqo &#zx
  → ‡) (q in A, q in C)
24:-: oxo 4 xxw 2 oxo 4 wxx &#zx
  = Wythoffian o3x3o4x (srit) with cell list:
        16 octs
        8  sircoes
        32 trips

related: .xo 4 .xw 2 .xo 4 .xx &#zx (cyted srit)
  → CRF with cell list:
        8  ops
        4  sircoes
        16 squippies (J1)
        16 trips
123:B13: xox 4 xww 2 xox 4 qqo &#zx
  → ‡) (q in A, w in C)
124:B1: xox 4 xww 2 oxo 4 wxx &#zx
  → ‡) (w in C)
1234:B13: xox 4 xww 2 xox 4 wwx &#zx
  → ‡) (w in A, w in C)


EKF of the hexadecachoron (x3o3o4o)

©

(As it will turn out, the set of resulting polychora in o2o3o4o resp. . o3o4o here is identical to those which turn up from the corresponding consideration of ico wrt. these subsymmetries.)

in o2o3o4o subsymmetry   (up)
Representation:
qo 2 ox 3 oo 4 oo &#zx  (hex)
All layers &
kaleido-facetings per layer:
A: q2o3o4o
B: o2x3o4o   →  B2:  o 2(-x)3  x 4 o   →  B23:  o 2  o 3(-x)4 q
A priori invalid combinations:
none
Stott expansion:
(derived potential CRFs)
1:-: wx 2 ox 3 oo 4 oo &#zx
  = oxxo 3 oooo 4 oooo &#xt
  → CRF with cell list:
        16 tets
        8  trips
2:B2: qo 2 xo 3 ox 4 oo &#zx
  = xox 3 oxo 4 ooo &#xt
  = Wythoffian x3o4o3o (ico) with cell list:
        24 octs
3:-: qo 2 ox 3 xx 4 oo &#zx
  = oxo 3 xxx 4 ooo &#xt
  → CRF with cell list:
        2  coes
        12 cubes
        16 tricues (J3)
3:B23: qo 2 oo 3 xo 4 oq &#zx
  = ooo 3 xox 4 oqo &#xt
  = Wythoffian o3o3x4o (rit) with cell list:
        8  coes
        16 tets
4:-: qo 2 ox 3 oo 4 xx &#zx
  = oxo 3 ooo 4 xxx &#xt
  → CRF with cell list:
        14 cubes
        16 tets
        24 trips
12:B2: wx 2 xo 3 ox 4 oo &#zx
  = xoox 3 oxxo 4 oooo &#xt
  → CRF with cell list:
        6  esquidpies (J15)
        18 octs
        8  trips
13:-: wx 2 ox 3 xx 4 oo &#zx
  = oxxo 3 xxxx 4 oooo &#xt
  → CRF with cell list:
        2  coes
        18 cubes
        8  hips
        16 tricues (J3)
13:B23: wx 2 oo 3 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: wx .. .. oq &#zx)
14:-: wx 2 ox 3 oo 4 xx &#zx
  = oxxo 3 oooo 4 xxxx &#xt
  = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips
23:B23: qo 2 xx 3 xo 4 oq &#zx
  = xxx 3 xox 4 oqo &#xt
  → CRF with cell list:
        6  coes
        12 cubes
        2  toes
        16 tricues (J3)
24:B2: qo 2 xo 3 ox 4 xx &#zx
  = xox 3 oxo 4 xxx &#xt
  → CRF with cell list:
        16 octs
        2  sircoes
        6  squobcues (J28)
        24 trips
34:-: qo 2 ox 3 xx 4 xx &#zx
  = oxo 3 xxx 4 xxx &#xt
  → CRF with cell list:
        12 ops
        2  tics
        16 tricues (J3)
        24 trips
34:B23: qo 2 oo 3 xo 4 xw &#zx
  → °) (asks for non-regular hexagons: qo .. .. xw &#zx)
123:B23: wx 2 xx 3 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: wx .. .. oq &#zx)
124:B2: wx 2 xo 3 ox 4 xx &#zx
  = xoox 3 oxxo 4 xxxx &#xt
  = Wythoffian o3x3o4x (srit) with cell list:
        16 octs
        8  sircoes
        32 trips
134:-: wx 2 ox 3 xx 4 xx &#zx
  = oxxo 3 xxxx 4 xxxx &#xt
  → CRF with cell list:
        12 cubes
        8  hips
        18 ops
        2  tics
        16 tricues (J3)
        24 trips
134:B23: wx 2 oo 3 xo 4 xw &#zx
  = oooo 3 xoox 4 xwwx &#xt
  = Wythoffian o3o3x4x (tat) with cell list:
        16 tets
        8  tics
234:B23: qo 2 xx 3 xo 4 xw &#zx
  → °) (asks for non-regular hexagons: qo .. .. xw &#zx)
1234:B23: wx 2 xx 3 xo 4 xw &#zx
  = xxxx 3 xoox 4 xwwx &#xt
  → CRF with cell list:
        2  gircoes
        12 ops
        6  tics
        16 tricues (J3)
        8  trips

in . o3o4o subsymmetry   (up)
additional,
not prismatically symmetric
combinations of formers:
none 


in . o3o3o subsymmetry   (up)
Representation:
xo 3 oo 3 ox &#x  (hex)
All layers &
kaleido-facetings per layer:
A: x3o3o   →  A1:(-x)3  x 3  o   →  A12:  o 3(-x)3  x   →  A123:  o 3  o 3(-x)
B: o3o3x   →  B3:  o 3  x 3(-x)  →  B32:  x 3(-x)3  o   →  B321:(-x)3  o 3  o
A priori invalid combinations:
A + B321  → ‡) (u in A)
A1 + B32  → ‡) (u in A, u in B)
A12 + B3  → ‡) (u in A, u in B) 
A123 + B  → ‡) (u in B)
Stott expansion:
(derived potential CRFs)
1:A1: ox 3 xo 3 ox &#x (octaco)
  → CRF (segmentochoron) with cell list:
        1 co
        9 octs
        6 squippies (J1)
1:A1B321: oo 3 xo 3 oo &#x (octpy)
  → CRF (segmentochoron) with cell list:
        1 oct
        8 tets
2:-: xo 3 xx 3 ox &#x (tutcup)
  → CRF (segmentochoron) with cell list:
        6 tets
        8 tricues (J3)
        2 tuts
2:A12: oo 3 ox 3 xx &#x (tetatut)
  → CRF (segmentochoron) with cell list:
        5 tets
        4 tricues (J3)
        1 tut
2:A12B32: ox 3 oo 3 xo &#x
  = Wythoffian x3o3o4o (hex) with cell list:
        16 tets
  (axially dual orientation)
12:A12: xx 3 ox 3 xx &#x (coatoe)
  → CRF (segmentochoron) with cell list:
        1 co
        6 cubes
        1 toe
        8 tricues (J3)
12:A12B321: xo 3 ox 3 xo &#x (octaco)
  → CRF (segmentochoron) with cell list:
        1 co
        9 octs
        6 squippies (J1)
13:A1B3: ox 3 xx 3 xo &#x (tutcup)
  → CRF (segmentochoron) with cell list:
        6 tets
        8 tricues (J3)
        2 tuts
13:A1B321: oo 3 xo 3 xx &#x (tetatut)
  → CRF (segmentochoron) with cell list:
        5 tets
        4 tricues (J3)
        1 tut
13:A123B321: xo 3 oo 3 ox &#x
  = Wythoffian x3o3o4o (hex) with cell list:
        16 tets
  (identical orientation)
123:A123B321: xo 3 xx 3 ox &#x (tutcup)
  → CRF (segmentochoron) with cell list:
        6 tets
        8 tricues (J3)
        2 tuts
 


in o4o2o4o subsymmetry   (up)
Representation:
xo 4 oo 2 ox 4 oo &#zx  (hex)
All layers &
kaleido-facetings per layer:
A: x4o o4o   →  A1: (-x)4 q   o 4 o
B: o4o x4o   →  B3:   o 4 o (-x)4 q
Stott expansion:
(derived potential CRFs)
1:A1: ox 4 qo 2 ox 4 oo &#zx
  → CRF with cell list:
        4  cubes
        4  octs
        16 squippies (J1)
2:-: xo 4 xx 2 ox 4 oo &#zx
  → CRF with cell list:
        4  cubes
        16 tets
        16 trips
12:A1: ox 4 wx 2 ox 4 oo &#zx
  → CRF with cell list:
        4  esquidpies (J15)
        4  ops
        16 squippies (J1)
13:A1B3: ox 4 qo 2 xo 4 oq &#zx
  = Wythoffian o3o3x4o (rit) with cell list:
        8  coes
        16 tets
14:A1: ox 4 qo 2 ox 4 xx &#zx
  → CRF with cell list:
        8  cubes
        16 squippies (J1)
        4  squobcues (J28)
        16 trips
24:-: xo 4 xx 2 ox 4 xx &#zx
  = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips
123:A1B3: ox 4 wx 2 xo 4 oq &#zx
  → °) (asks for non-regular hexagons: .. wx .. oq &#zx)
124:A1: ox 4 wx 2 ox 4 xx &#zx
  → CRF with cell list:
        8  ops
        4  sircoes
        16 squippies (J1)
        16 trips
1234:A1B3: ox 4 wx 2 xo 4 xw &#zxx
  = Wythoffian o3o3x4x (tat) with cell list:
        16 tets
        8  tics



in o2o2o2o subsymmetry   (up)
Representation:
qooo 2 oqoo 2 ooqo 2 oooq &#zx  (hex)
All layers &
kaleido-facetings per layer:
A: q2o2o2o
B: o2q2o2o
C: o2o2q2o
D: o2o2o2q

(As this representation does not show up (true / x-) edges within the layers, those thus cannot be inverted either. 
Therefore at most pure partial Stott expansions wrt. this subsymmetry remain possible.)
Stott expansion:
(derived potential CRFs)
1:A1: wxxx 2 oqoo 2 ooqo 2 oooq &#zx (pexhex)
  → CRF with cell list:
        16 tets
        8  trips

related: .xxx 2 .qoo 2 .oqo 2 .ooq &#zx
  = Wythoffian x x3o4o (ope) with cell list:
        2 octs
        8 trips
12:-: wxxx 2 xwxx 2 ooqo 2 oooq &#zx (quawros)
  → CRF with cell list:
        4  cubes
        16 tets
        16 trips
123:-: wxxx 2 xwxx 2 xxwx 2 oooq &#zx (pacsid pith)
  → CRF with cell list:
        14 cubes
        16 tets
        24 trips
1234:-: wxxx 2 xwxx 2 xxwx 2 xxxw &#zx
  = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips

related: .xxx 2 .wxx 2 .xwx 2 .xxw &#zx
  = Wythoffian x x3o4x (sircope) with cell list:
        18 cubes
        2  sircoes
        8  trips


EKF of the pentachoron (x3o3o3o)

©

in . o3o3o subsymmetry   (up)
Representation:
ox 3 oo 3 oo &#x  (pen)
All layers &
kaleido-facetings per layer:
A: o3o3o
B: x3o3o   →  B1:(-x)3  x 3  o   →  B12:  o 3(-x)3  x   →  B123:  o 3  o 3(-x)
A priori invalid combinations:
none
Stott expansion:
(derived potential CRFs)
1:B1: xo 3 ox 3 oo &#x
  = Wythoffian o3x3o4o (rap) with cell list:
        5 octs
        5 tets
2:-: ox 3 xx 3 oo &#x
  → CRF (segmentochoron) with cell list:
        1 oct
        4 tricues (J3)
        4 trips
        1 tut
2:B12: oo 3 xo 3 ox &#x
  = Wythoffian o3x3o3o (rap) with cell list:
        5 octs
        5 tets
  (inverted orientation)
3:-: ox 3 oo 3 xx &#x
  → CRF (segmentochoron) with cell list:
        1  co
        5  tets
        10 trips
3:B123: oo 3 oo 3 xo &#x
  = Wythoffian o3o3o3x (pen) with cell list:
        5 tets
  (dual orientation)
12:B12: xx 3 xo 3 ox &#x
  → CRF (segmentochoron) with cell list:
        1 co
        4 octs
        4 tricues (J3)
        6 trips
        1 tut
13:B1: xo 3 ox 3 xx &#x
  → CRF (segmentochoron) with cell list:
        1 co
        4 octs
        4 tricues (J3)
        6 trips
        1 tut
  (inverted orientation)
13:B123: xx 3 oo 3 xo &#x
  → CRF (segmentochoron) with cell list:
        1  co
        5  tets
        10 trips
  (inverted orientation)
23:-: ox 3 xx 3 xx &#x
  → CRF (segmentochoron) with cell list:
        4 hips
        1 toe
        4 tricues (J3)
        6 trips
        1 tut
23:B123: oo 3 xx 3 xo &#x
  → CRF (segmentochoron) with cell list:
        1 oct
        4 tricues (J3)
        4 trips
        1 tut
123:B123: xx 3 xx 3 xo &#x
  → CRF (segmentochoron) with cell list:
        4 hips
        1 toe
        4 tricues (J3)
        6 trips
        1 tut
  (inverted orientation)



EKF of the small rhombated pentachoron (x3o3x3o)

  ©
(seen oct first   –     seen co first)

(As it will turn out, the set of resulting polychora in . o3o3o here is identical to those which turn up from the corresponding consideration of spid wrt. this subsymmetry.)

in . o3o3o subsymmetry   (up)
Representation:
oxx 3 xxo 3 oox &#xt  (srip)
All layers &
kaleido-facetings per layer:
A: o3x3o   →  A2:  x 3(-x)3  x   →  A21: (-x)3  o 3  x   →  A213: (-x)3  x 3(-x)   →  A2132:  o 3(-x)3 o
                                 ↳  A23:   x 3  o 3(-x)  →  (A231 = A213)          →  (A2312 = A2132)
B: x3x3o   →  B1:(-x)3  u 3  o
           ↳  B2:  u 3(-x)3  x   →  B23:   u 3  o 3(-x)
C: x3o3x   →  C1:(-x)3  x 3  x   →  C12:   o 3(-x)3  u
                                 ↳  C13: (-x)3  u 3(-x)
           ↳  C3:  x 3  x 3(-x)  →  (C31 = C13)
                                 ↳  C32:   u 3(-x)3  o
A priori invalid combinations:
A     + B2,B23
A     + C12,C32
A2    + B,B1,B23
A2    + C1,C3,C13
A21   + B,B1,B2,B23 → generally
A23   + B1,B2
A23   + C,C1,C12
A213  + B,B2,B23
A213  + C,C1,C3,C12,C32
A2132 + B,B1,B2,B23 → generally
B     + C1,C12,C13,C32
B1    + C,C3,C12,C32
B2    + C1,C3,C12,C32
B23   + C,C1,C12,C13
C12   generally (u in extremal layer)
C13   generally (u in extremal layer)
C32   generally (u in extremal layer)
Other layer-combinations:
B1C1:     o(-x)(-x) 3 xux 3 oox &#xt
A2B2:     xux 3 (-x)(-x)o 3 xxx &#xt
C3:       oxx 3 xxx 3 oo(-x) &#xt
A23C3:    xxx 3 oxx 3 (-x)o(-x) &#xt  → †)
A23B23C3: xux 3 oox 3 (-x)(-x)(-x) &#xt
Stott expansion:
(derived potential CRFs)
1:B1C1: xoo 3 xux 3 oox &#xt
  = Wythoffian o3x3x3o (deca) with cell list:
        10 tuts
2:A2B2: xux 3 oox 3 xxx &#xt
  → CRF with cell list:
        1 co
        6 hips
        1 toe
        4 tricues (J3)
        4 trips
        4 tuts
3:C3: oxx 3 xxx 3 xxo &#xt
  → CRF with cell list:
        8  hips
        8  tricues (J3)
        12 trips
        2  tuts
  (bistratic segmentochoral stack)

related: ox. 3 xx. 3 xx. &#x (tutatoe)
  → CRF (segmentochoron) with cell list:
        4 hips
        1 toe
        4 tricues (J3)
        6 trips
        1 tut
3:A23B23C3: xux 3 oox 3 ooo &#xt
  = Wythoffian x3x3o3o (tip) with cell list:
        5 tets
        5 tuts


EKF of the small prismatodecachoron (x3o3o3x)

©

(As it will turn out, the set of resulting polychora in . o3o3o here is identical to those which turn up from the corresponding consideration of srip wrt. this subsymmetry.)

in . o3o3o subsymmetry   (up)
Representation:
xxo 3 ooo 3 oxx &#xt  (spid)
All layers &
kaleido-facetings per layer:
A: x3o3o   →  A1: (-x)3  x 3  o   →  A12:   o 3(-x)3  x   →  A123:   o 3  o 3(-x)
B: x3o3x   →  B1: (-x)3  x 3  x   →  B12:   o 3(-x)3  u
                                  ↳  B13: (-x)3  u 3(-x)
           ↳  B3:   x 3  x 3(-x)  →  (B31 = B13)
                                  ↳  B32:   u 3(-x)3  o
C: o3o3x   →  C3:   o 3  x 3(-x)  →  C32:   x 3(-x)3  o   →  C321: (-x)3  o 3  o
A priori invalid combinations:
A    + B1,B12,B13
A1   + B,B3,B12,B32
A1   + C32
A12  + B1,B3,B13,B32
A12  + C3
A123 + B,B1,B12,B13,B32
A123 + C
B    + C3,C321
B1   + C3,C32
B3   + C,C32,C321
B12  + C3,C32,C321
B13  + C,C32,C321
B32  + C,C3,C321
Other layer-combinations:
A1B1:     (-x)(-x)o 3 xxo 3 oxx &#xt
A12:      oxo 3 (-x)oo 3 xxx &#xt  → †)
A12B12:   ooo 3 (-x)(-x)o 3 xux &#xt
A12C32:   oxx 3 (-x)o(-x) 3 xxo &#xt  → †)
A123B3C3: oxo 3 oxx 3 (-x)(-x)(-x) &#xt  → †)
A1B13C3:  (-x)(-x)o 3 xux 3 o(-x)(-x) &#xt
Stott expansion:
(derived potential CRFs)
1:A1B1: oox 3 xxo 3 oxx &#xt
  = Wythoffian x3o3x3o (srip) with cell list:
        5  coes
        5  octs
        10 trips

related: .ox 3 .xo 3 .xx &#x (coatut)
  → CRF (segmentochoron) with cell list:
        1 co
        4 octs
        4 tricues (J3)
        6 trips
        1 tut

related: oo. 3 xx. 3 ox. &#x (octatut)
  → CRF (segmentochoron) with cell list:
        1 oct
        4 tricues (J3)
        4 trips
        1 tut
2:-: xxo 3 xxx 3 oxx &#xt
  → CRF with cell list:
        8  hips
        8  tricues (J3)
        12 trips
        2  tuts
  (bistratic segmentochoral stack)

related: xx. 3 xx. 3 ox. &#x (tutatoe)
  → CRF (segmentochoron) with cell list:
        4 hips
        1 toe
        4 tricues (J3)
        6 trips
        1 tut
2:A12B12: ooo 3 oox 3 xux &#xt
  = Wythoffian x3x3o3o (tip) with cell list:
        5 tets
        5 tuts
13:A1B13C3: xoo 3 xux 3 oox &#xt
  = Wythoffian o3x3x3o (deca) with cell list:
        10 tuts

in . o2o3o subsymmetry   (up)
Representation:
x(ou)x 2 x(xo)o 3 o(xo)x &#xt  (spid)
All layers &
kaleido-facetings per layer:
A: x2x3o   →  A1: (-x)2  x 3  o   →  A12: (-x)2(-x)3  x   →  A123: (-x)2  o 3(-x)
           ↳  A2:   x 2(-x)3  x   →  (A21 = A12)
                                  ↳  A23:   x 2  o 3(-x)  →  (A231 = A123)
B: o2x3x   →  B2:   o 2(-x)3  u
           ↳  B3:   o 2  u 3(-x)
C: u2o3o
D: x2o3x   →  D1: (-x)2  o 3  x   →  D13: (-x)2  x 3(-x)  →  D132: (-x)2(-x)3  o
           ↳  D3:   x 2  x 3(-x)  →  (D31 = D13)
                                  ↳  D32:   x 2(-x)3  o   →  (D321 = D132)
A priori invalid combinations:
A    + B2,D1,D13,D32,D132
A1   + B2,D,D3,D32,D132
A2   + B,B3,D1,D3,D13,D132
A12  + B,B3,D,D3,D13,D32
A23  + B,D,D1,D13,D132
A123 + B,D,D1,D3,D32
B    + D3,D13,D32,D132
B2   + D3,D13
B3   + D,D1
Other layer-combinations:
B3D3       x(ou)x 2 x(uo)x 3 o((-x)o)(-x) &#xt
A1D1       (-x)(ou)(-x) 2 x(xo)o 3 o(xo)x &#xt  → †
A1B3D13    (-x)(ou)(-x) 2 x(uo)x 3 o((-x)o)(-x) &#xt  → †
A2B2D32    x(ou)x 2 (-x)((-x)o)(-x) 3 x(uo)o &#xt  → †
A12B2D132  (-x)(ou)(-x) 2 (-x)((-x)o)(-x) 3 x(uo)o &#xt  → †
A23B2D32   x(ou)x 2 o((-x)o)(-x) 3 (-x)(uo)o &#xt  → †
A123B2D132 (-x)(ou)(-x) 2 o((-x)o)(-x) 3 (-x)(uo)o &#xt  → †
Stott expansion:
(derived potential CRFs)
3:B3D3: x(ou)x 2 x(uo)x 3 x(ox)o &#xt
  → CRF with cell list:
        3 coes
        1 hip
        2 oct
        3 squippies (J1)
        2 tricues (J3)
        7 trips


EKF of the rectified hexacosachoron (o3x3o5o)

©

in o2o3o5o subsymmetry   (up)
Representation:
DCBAVFfxoo 2 xoxFofofVx 3 oxoofoxxoo 5 ooxooxxoof &#zx  (rox)
All layers &
kaleido-facetings per layer:
A: D2x3o5o   →  A2: D2(-x)3x5o   →  A23: D2o3(-x)5f
B: C2o3x5o   →  B3: C2x3(-x)5f   →  B32: C2(-x)3o5f
C: B2x3o5x   →  C2: B2(-x)3x5x   →  C23: B2o3(-x)5F
                                 ↳  C24: B2(-x)3F5(-x)
             ↳  C4: B2x3f5(-x)   →  (C42 = C24)
D: A2F3o5o
E: V2o3f5o
F: F2f3o5x   →  F4: F2f3f5(-x)
G: f2o3x5x   →  G3: f2x3(-x)5F   →  G32: f2(-x)3o5F
             ↳  G4: f2o3F5(-x)
H: x2f3x5o   →  H1: (-x)2f3x5o   →  H13: (-x)2F3(-x)5f
             ↳  H3: x2F3(-x)5f   →  (H31 = H13)
I: o2V3o5o
i: o2x3o5f   →  i2: o2(-x)3x5f   →  i23: o2o3(-x)5V

(Note, I and i both belong to the same hyperplane o2... .)
A priori invalid combinations:
A   + B32, C2, C24, G32, i2
A2  + B3, C, C4, C23, G3, H3, H13, i, i23
A23 + B, C2, G, H, H1, i2
B   + C23, G3, H3, H13, i23
B3  + C2, C24, G, G32, H, H1, i2
B32 + C, C4, G3, i
C   + F4, G4, G32, i2
C2  + F4, G3, G4, H3, H13, i, i23
C4  + F, G, G32, i2
C23 + G, H, H1, i2
C24 + F, G, G3, i
F   + G4
F4  + G
G   + H3, H13, i23
G3  + H, H1, i2
G32 + i
H   + i23
H1  + i23
H3  + i2
H13 + i2

(all these would provide u edges (→ ‡); thus reducing from 4320 to 70 potential combinations only)
Other layer-combinations:
H1:                   DCBAVFf(-x)oo 2 xoxFofofVx 3 oxoofoxxoo 5 ooxooxxoof &#zx  → †) (dead end at I)
C4F4G4:               DCBAVFfxoo 2 xoxFofofVx 3 oxfoffFxoo 5 oo(-x)oo(-x)(-x)oof &#zx  → ‡ (f in C, E, F)
C4F4G4H1:             DCBAVFf(-x)oo 2 xoxFofofVx 3 oxfoffFxoo 5 oo(-x)oo(-x)(-x)oof &#zx  → †)
B3G3H3:               DCBAVFfxoo 2 xxxFofxFVx 3 o(-x)oofo(-x)(-x)oo 5 ofxooxFfof &#zx  → ‡ (f in G, i)
B3G3H3i23:            DCBAVFfxoo 2 xxxFofxFVo 3 o(-x)oofo(-x)(-x)o(-x) 5 ofxooxFfoV &#zx
B3G3H13:              DCBAVFf(-x)oo 2 xxxFofxFVx 3 o(-x)oofo(-x)(-x)oo 5 ofxooxFfof &#zx  → †) (dead end at I)
B3G3H13i23:           DCBAVFf(-x)oo 2 xxxFofxFVo 3 o(-x)oofo(-x)(-x)o(-x) 5 ofxooxFfoV &#zx  → †) (dead end at I)
B3C4F4G3H3:           DCBAVFfxoo 2 xxxFofxFVx 3 o(-x)foff(-x)(-x)oo 5 of(-x)oo(-x)Ffof &#zx  → †)
B3C4F4G3H3i23:        DCBAVFfxoo 2 xxxFofxFVo 3 o(-x)foff(-x)(-x)o(-x) 5 of(-x)oo(-x)FfoV &#zx  → †)
B3C4F4G3H13:          DCBAVFf(-x)oo 2 xxxFofxFVx 3 o(-x)foff(-x)(-x)oo 5 of(-x)oo(-x)Ffof &#zx  → †)
B3C4F4G3H13i23:       DCBAVFf(-x)oo 2 xxxFofxFVo 3 o(-x)foff(-x)(-x)o(-x) 5 of(-x)oo(-x)FfoV &#zx  → †)
B3C4F4G4H3:           DCBAVFfxoo 2 xxxFofoFVx 3 o(-x)foffF(-x)oo 5 of(-x)oo(-x)(-x)fof &#zx  → †)
B3C4F4G4H3i23:        DCBAVFfxoo 2 xxxFofoFVo 3 o(-x)foffF(-x)o(-x) 5 of(-x)oo(-x)(-x)foV &#zx  → †)
B3C4F4G4H13:          DCBAVFf(-x)oo 2 xxxFofoFVx 3 o(-x)foffF(-x)oo 5 of(-x)oo(-x)(-x)fof &#zx  → †)
B3C4F4G4H13i23:       DCBAVFf(-x)oo 2 xxxFofoFVo 3 o(-x)foffF(-x)o(-x) 5 of(-x)oo(-x)(-x)foV &#zx  → †)
B3C23G3H3:            DCBAVFfxoo 2 xxoFofxFVx 3 o(-x)(-x)ofo(-x)(-x)oo 5 ofFooxFfof &#zx  → †)
B3C23G3H3i23:         DCBAVFfxoo 2 xxoFofxFVo 3 o(-x)(-x)ofo(-x)(-x)o(-x) 5 ofFooxFfoV &#zx  → †)
B3C23G3H13:           DCBAVFf(-x)oo 2 xxoFofxFVx 3 o(-x)(-x)ofo(-x)(-x)oo 5 ofFooxFfof &#zx  → †)
B3C23G3H13i23:        DCBAVFf(-x)oo 2 xxoFofxFVo 3 o(-x)(-x)ofo(-x)(-x)o(-x) 5 ofFooxFfoV &#zx  → †)
A2C2i2:               DCBAVFfxoo 2 (-x)o(-x)FofofV(-x) 3 xxxofoxxox 5 ooxooxxoof &#zx  → †) (dead end at D)
A2C2H1i2:             DCBAVFf(-x)oo 2 (-x)o(-x)FofofV(-x) 3 xxxofoxxox 5 ooxooxxoof &#zx  → †)
A2C2G32i2:            DCBAVFfxoo 2 (-x)o(-x)Fof(-x)fV(-x) 3 xxxofooxox 5 ooxooxFoof &#zx  → †)
A2C2G32H1i2:          DCBAVFf(-x)oo 2 (-x)o(-x)Fof(-x)fV(-x) 3 xxxofooxox 5 ooxooxFoof &#zx  → †)
A2C24F4G4i2:          DCBAVFfxoo 2 (-x)o(-x)FofofV(-x) 3 xxFoffFxox 5 oo(-x)oo(-x)(-x)oof &#zx  → †) (dead end at D)
A2C24F4G4H1i2:        DCBAVFf(-x)oo 2 (-x)o(-x)FofofV(-x) 3 xxFoffFxox 5 oo(-x)oo(-x)(-x)oof &#zx  → †) (dead end at D)
A2C24F4G32i2:         DCBAVFfxoo 2 (-x)o(-x)Fof(-x)fV(-x) 3 xxFoffoxox 5 oo(-x)oo(-x)Foof &#zx  → †) (dead end at D)
A2C24F4G32H1i2:       DCBAVFf(-x)oo 2 (-x)o(-x)Fof(-x)fV(-x) 3 xxFoffoxox 5 oo(-x)oo(-x)Foof &#zx  → †) (dead end at D)
A2B32C2i2:            DCBAVFfxoo 2 (-x)(-x)(-x)FofofV(-x) 3 xoxofoxxox 5 ofxooxxoof &#zx  → †) (dead end at D)
A2B32C2H1i2:          DCBAVFf(-x)oo 2 (-x)(-x)(-x)FofofV(-x) 3 xoxofoxxox 5 ofxooxxoof &#zx  → †) (dead end at D)
A2B32C2G32i2:         DCBAVFfxoo 2 (-x)(-x)(-x)Fof(-x)fV(-x) 3 xoxofooxox 5 ofxooxFoof &#zx  → †) (dead end at D)
A2B32C2G32H1i2:       DCBAVFf(-x)oo 2 (-x)(-x)(-x)Fof(-x)fV(-x) 3 xoxofooxox 5 ofxooxFoof &#zx  → †) (dead end at D)
A2B32C24F4G4i2:       DCBAVFfxoo 2 (-x)(-x)(-x)FofofV(-x) 3 xoFoffFxox 5 of(-x)oo(-x)(-x)oof &#zx  → †)
A2B32C24F4G4H1i2:     DCBAVFf(-x)oo 2 (-x)(-x)(-x)FofofV(-x) 3 xoFoffFxox 5 of(-x)oo(-x)(-x)oof &#zx  → †)
A2B32C24F4G32i2:      DCBAVFfxoo 2 (-x)(-x)(-x)Fof(-x)fV(-x) 3 xoFoffoxox 5 of(-x)oo(-x)Foof &#zx  → †)
A2B32C24F4G32H1i2:    DCBAVFf(-x)oo 2 (-x)(-x)(-x)Fof(-x)fV(-x) 3 xoFoffoxox 5 of(-x)oo(-x)Foof &#zx  → †)
A23B3G3H3:            DCBAVFfxoo 2 oxxFofxFVx 3 (-x)(-x)oofo(-x)(-x)oo 5 ffxooxFfof &#zx  → ‡ (f in A)
A23B3G3H3i23:         DCBAVFfxoo 2 oxxFofxFVo 3 (-x)(-x)oofo(-x)(-x)o(-x) 5 ffxooxFfoV &#zx  → ‡ (f in A)
A23B3G3H13:           DCBAVFf(-x)oo 2 oxxFofxFVx 3 (-x)(-x)oofo(-x)(-x)oo 5 ffxooxFfof &#zx  → ‡ (f in A)
A23B3G3H13i23:        DCBAVFf(-x)oo 2 oxxFofxFVo 3 (-x)(-x)oofo(-x)(-x)o(-x) 5 ffxooxFfoV &#zx  → ‡ (f in A)
A23B3C4F4G3H3:        DCBAVFfxoo 2 oxxFofxFVx 3 (-x)(-x)foff(-x)(-x)oo 5 ff(-x)oo(-x)Ffof &#zx  → ‡ (F in A)
A23B3C4F4G3H3i23:     DCBAVFfxoo 2 oxxFofxFVo 3 (-x)(-x)foff(-x)(-x)o(-x) 5 ff(-x)oo(-x)FfoV &#zx  → ‡ (F in A)
A23B3C4F4G3H13:       DCBAVFf(-x)oo 2 oxxFofxFVx 3 (-x)(-x)foff(-x)(-x)oo 5 ff(-x)oo(-x)Ffof &#zx  → ‡ (F in A)
A23B3C4F4G3H13i23:    DCBAVFf(-x)oo 2 oxxFofxFVo 3 (-x)(-x)foff(-x)(-x)o(-x) 5 ff(-x)oo(-x)FfoV &#zx  → ‡ (F in A)
A23B3C4F4G4H3:        DCBAVFfxoo 2 oxxFofoFVx 3 (-x)(-x)foffF(-x)oo 5 ff(-x)oo(-x)(-x)fof &#zx  → ‡ (F in A)
A23B3C4F4G4H3i23:     DCBAVFfxoo 2 oxxFofoFVo 3 (-x)(-x)foffF(-x)o(-x) 5 ff(-x)oo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B3C4F4G4H13:       DCBAVFf(-x)oo 2 oxxFofoFVx 3 (-x)(-x)foffF(-x)oo 5 ff(-x)oo(-x)(-x)fof &#zx  → ‡ (F in A)
A23B3C4F4G4H13i23:    DCBAVFf(-x)oo 2 oxxFofoFVo 3 (-x)(-x)foffF(-x)o(-x) 5 ff(-x)oo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B3C23G3H3:         DCBAVFfxoo 2 oxoFofxFVx 3 (-x)(-x)(-x)ofo(-x)(-x)oo 5 ffFooxFfof &#zx  → ‡ (f in A)
A23B3C23G3H3i23:      DCBAVFfxoo 2 oxoFofxFVo 3 (-x)(-x)(-x)ofo(-x)(-x)o(-x) 5 ffFooxFfoV &#zx  → ‡ (f in A)
A23B3C23G3H13:        DCBAVFf(-x)oo 2 oxoFofxFVx 3 (-x)(-x)(-x)ofo(-x)(-x)oo 5 ffFooxFfof &#zx  → ‡ (f in A)
A23B3C23G3H13i23:     DCBAVFf(-x)oo 2 oxoFofxFVo 3 (-x)(-x)(-x)ofo(-x)(-x)o(-x) 5 ffFooxFfoV &#zx  → ‡ (f in A)
A23B3C23F4G3H3:       DCBAVFfxoo 2 oxoFofxFVx 3 (-x)(-x)(-x)off(-x)(-x)oo 5 ffFoo(-x)Ffof &#zx  → ‡ (F in A)
A23B3C23F4G3H3i23:    DCBAVFfxoo 2 oxoFofxFVo 3 (-x)(-x)(-x)off(-x)(-x)o(-x) 5 ffFoo(-x)FfoV &#zx  → ‡ (F in A)
A23B3C23F4G3H13:      DCBAVFf(-x)oo 2 oxoFofxFVx 3 (-x)(-x)(-x)off(-x)(-x)oo 5 ffFoo(-x)Ffof &#zx  → ‡ (F in A)
A23B3C23F4G3H13i23:   DCBAVFf(-x)oo 2 oxoFofxFVo 3 (-x)(-x)(-x)off(-x)(-x)o(-x) 5 ffFoo(-x)FfoV &#zx  → ‡ (F in A)
A23B3C23F4G4H3:       DCBAVFfxoo 2 oxoFofoFVx 3 (-x)(-x)(-x)offF(-x)oo 5 ffFoo(-x)(-x)fof &#zx  → ‡ (F in A)
A23B3C23F4G4H3i23:    DCBAVFfxoo 2 oxoFofoFVo 3 (-x)(-x)(-x)offF(-x)o(-x) 5 ffFoo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B3C23F4G4H13:      DCBAVFf(-x)oo 2 oxoFofoFVx 3 (-x)(-x)(-x)offF(-x)oo 5 ffFoo(-x)(-x)fof &#zx  → ‡ (F in A)
A23B3C23F4G4H13i23:   DCBAVFf(-x)oo 2 oxoFofoFVo 3 (-x)(-x)(-x)offF(-x)o(-x) 5 ffFoo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B32C23G32H3i23:    DCBAVFfxoo 2 o(-x)oFof(-x)FVo 3 (-x)o(-x)ofoo(-x)o(-x) 5 ffFooxFfoV &#zx  → ‡ (f in A)
A23B32C23G32H13i23:   DCBAVFf(-x)oo 2 o(-x)oFof(-x)FVo 3 (-x)o(-x)ofoo(-x)o(-x) 5 ffFooxFfoV &#zx  → ‡ (f in A)
A23B32C23F4G4H3i23:   DCBAVFfxoo 2 o(-x)oFofoFVo 3 (-x)o(-x)offF(-x)o(-x) 5 ffFoo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B32C23F4G4H13i23:  DCBAVFf(-x)oo 2 o(-x)oFofoFVo 3 (-x)o(-x)offF(-x)o(-x) 5 ffFoo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B32C23F4G32H3i23:  DCBAVFfxoo 2 o(-x)oFof(-x)FVo 3 (-x)o(-x)offo(-x)o(-x) 5 ffFoo(-x)FfoV &#zx  → ‡ (F in A)
A23B32C23F4G32H13i23: DCBAVFf(-x)oo 2 o(-x)oFof(-x)FVo 3 (-x)o(-x)offo(-x)o(-x) 5 ffFoo(-x)FfoV &#zx  → ‡ (F in A)
A23B32C24F4G4H3i23:   DCBAVFfxoo 2 o(-x)(-x)FofoFVo 3 (-x)oFoffF(-x)o(-x) 5 ff(-x)oo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B32C24F4G4H13i23:  DCBAVFf(-x)oo 2 o(-x)(-x)FofoFVo 3 (-x)oFoffF(-x)o(-x) 5 ff(-x)oo(-x)(-x)foV &#zx  → ‡ (F in A)
A23B32C24F4G32H3i23:  DCBAVFfxoo 2 o(-x)(-x)Fof(-x)FVo 3 (-x)oFoffo(-x)o(-x) 5 ff(-x)oo(-x)FfoV &#zx  → ‡ (F in A)
A23B32C24F4G32H13i23: DCBAVFf(-x)oo 2 o(-x)(-x)Fof(-x)FVo 3 (-x)oFoffo(-x)o(-x) 5 ff(-x)oo(-x)FfoV &#zx  → ‡ (F in A)
Stott expansion:
(derived CRFs)
3:B3G3H3i23: DCBAVFfxoo 2 xxxFofxFVo 3 xoxxFxooxo 5 ofxooxFfoV &#zx
  → CRF with cell list:
        30  ids
        120 octs
        60  pips
        48  pocuroes (J32)
        60  squippies (J1)
        220 tets
        40  thawroes (J92)
        2   ties
        80  tricues (J3)
        120 trips

related: ..BAVFfxoo 2 ..xFofxFVo 3 ..xxFxooxo 5 ..xooxFfoV &#zx
  → CRF with cell list:
        2   grids
        30  ids
        120 octs
        24  pecues (J5)
        24  pocuroes (J32)
        60  squippies (J1)
        220 tets
        40  thawroes (J92)
        120 trips
                                                                                                           
in . o3o5o subsymmetry   (up)
additional,
not prismatically symmetric
combinations of formers:
none 

(As there are just 2 symmetrical combinations - rox and that single CRF - which differ in their equatorial sections
there is no further combination of resp. hemiglomes either.)
using here node marks / (pseudo) edge lengths: F=f+x=ff, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x=fff, C=2F=2f+2x, D=F+V=3f+x

in o3o3o *b3o subsymmetry   (up)
Representation:
Voo|Fxf|ofx 3 xxx|ooo|fff 3 oVo|fFx|xof *b3 ooV|xfF|fxo &#zx  (rox)

with cyclical layer symmetries: A(134) → B(341) → C(413) → A(134)
                                C(134) → D(341) → E(413) → C(134)
                                G(134) → H(341) → I(413) → G(134)
All layers &
kaleido-facetings per layer:
A: V3x3o *b3o   →  A2: B3(-x)3x *b3x   →  A23: B3o3(-x) *b3x   →  A234: B3x3(-x) *b3(-x)   →  A2342: C3(-x)3o *b3o
                                       ↳  A24: B3o3x *b3(-x)   →  (A243.. = A234..)
B: o3x3V *b3o   →  B2: x3(-x)3B *b3x   →  B21: (-x)3o3B *b3x   →  B214: (-x)3x3B *b3(-x)   →  B2142: o3(-x)3C *b3o
                                       ↳  B24: x3o3B *b3(-x)   →  (B241.. = B214..)
C: o3x3o *b3V   →  C2: x3(-x)3x *b3B   →  C21: (-x)3o3x *b3B   →  C213: (-x)3x3(-x) *b3B   →  C2132: o3(-x)3o *b3C
                                       ↳  C23: x3o3(-x) *b3B   →  (C231.. = C213..)
D: F3o3f *b3x   →  D4: F3x3f *b3(-x)   →  D42: A3(-x)3F *b3o
E: x3o3F *b3f   →  E1: (-x)3x3F *b3f   →  E12: o3(-x)3A *b3F
F: f3o3x *b3F   →  F3: f3x3(-x) *b3F   →  F32: F3(-x)3o *b3A
G: o3f3x *b3f   →  G3: o3F3(-x) *b3f
H: f3f3o *b3x   →  H4: f3F3o *b3(-x)
I: x3f3f *b3o   →  I1: (-x)3F3f *b3o
A priori invalid combinations:
A     + B2, B2142, C2, C2132, D42, E12, F32
A2    + B, B214, B24, C, C213, C23, D4, E1, F3, G3, H4
A23   + B214, B24, C2, C21, D4, F, G, H4
A234  + B2, B21, B2142, C2, C21, C2132, D, D42, E12, F, G, H
A2342 + B, B214, C, C213, D4, E1, F3
A24   + B2, B21, C213, C23, D, F3, G3, H
B     + C2, C2132, D42, E12, F32
B2    + C, C21, C213, D4, E1, F3, H4, I1
B21   + C2, C23, D4, E, H4, I
B214  + C2, C2132, C23, D, D42, E, E12, F32, H, I
B2142 + C, C213, D4, E1, F3
B24   + C21, C213, D, E1, H, I1
C     + D42, E12, F32
C2    + D4, E1, F3, G3, I1
C21   + E, F3, G3, I
C213  + D42, E, E12, F, F32, G, I
C2132 + D4, E1, F3
C23   + E1, F, G, I1
D   + H4
D4  + E12, F32, H
D42 + E1, F3
E   + I1
E1  + F32, I
E12 + F3
F   + G3
F3  + G








(all these would provide u edges (→ ‡); thus reducing
from 46655 to 175 other potential combinations only)
Other layer-combinations:
ABCDEF3G3HI:                    VooFxfofx3xxxooxFff3oVofF(-x)(-x)of *b3ooVxfFfxo&#zx → ‡ (f in D)
ABCDE1F3G3HI1:                  VooF(-x)fof(-x)3xxxxoxFfF3oVofF(-x)(-x)of *b3ooVxfFfxo&#zx → †
ABCD4E1F3G3H4I1:                VooF(-x)fof(-x)3xxxxxxFFF3oVofF(-x)(-x)of *b3ooV(-x)fFf(-x)o&#zx → †
ABC21DE1FGHI1:                  Vo(-x)F(-x)fof(-x)3xxooxoffF3oVxfFxxof *b3ooBxfFfxo&#zx → †
ABC21D4E1FGH4I1:                Vo(-x)F(-x)fof(-x)3xxoxxofFF3oVxfFxxof *b3ooB(-x)fFf(-x)o&#zx → †
ABC213DE1F3G3HI1:               Vo(-x)F(-x)fof(-x)3xxxoxxFfF3oV(-x)fF(-x)(-x)of *b3ooBxfFfxo&#zx → †
ABC213D4E1F3G3H4I1:             Vo(-x)F(-x)fof(-x)3xxxxxxFFF3oV(-x)fF(-x)(-x)of *b3ooB(-x)fFf(-x)o&#zx → †
ABC23DEF3G3HI:                  VoxFxfofx3xxoooxFff3oV(-x)fF(-x)(-x)of *b3ooBxfFfxo&#zx → ‡ (f in D)
ABC23D4EF3G3H4I:                VoxFxfofx3xxoxoxFFf3oV(-x)fF(-x)(-x)of *b3ooB(-x)fFf(-x)o&#zx → †
AB21C21DE1FGHI1:                V(-x)(-x)F(-x)fof(-x)3xoooxoffF3oBxfFxxof *b3oxBxfFfxo&#zx → †
AB21C213DE1F3G3HI1:             V(-x)(-x)F(-x)fof(-x)3xoxoxxFfF3oB(-x)fF(-x)(-x)of *b3oxBxfFfxo&#zx → †
AB214CD4E1FGH4I1:               V(-x)oF(-x)fof(-x)3xxxxxofFF3oBofFxxof *b3o(-x)V(-x)fFf(-x)o&#zx → †
AB214CD4E1F3G3H4I1:             V(-x)oF(-x)fof(-x)3xxxxxxFFF3oBofF(-x)(-x)of *b3o(-x)V(-x)fFf(-x)o&#zx → †
AB214C21D4E1FGH4I1:             V(-x)(-x)F(-x)fof(-x)3xxoxxofFF3oBxfFxxof *b3o(-x)B(-x)fFf(-x)o&#zx → †
AB214C213D4E1F3G3H4I1:          V(-x)(-x)F(-x)fof(-x)3xxxxxxFFF3oB(-x)fF(-x)(-x)of *b3o(-x)B(-x)fFf(-x)o&#zx → †
AB24C23D4EF3G3H4I:              VxxFxfofx3xooxoxFFf3oB(-x)fF(-x)(-x)of *b3o(-x)B(-x)fFf(-x)o&#zx → †
A2B2C2DEFGHI:                   BxxFxfofx3(-x)(-x)(-x)ooofff3xBxfFxxof *b3xxBxfFfxo&#zx
A2B2C2DEF32GHI:                 BxxFxFofx3(-x)(-x)(-x)oo(-x)fff3xBxfFoxof *b3xxBxfAfxo&#zx → †
A2B2C2DE12F32GHI:               BxxFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3xBxfAoxof *b3xxBxFAfxo&#zx → †
A2B2C2D42E12F32GHI:             BxxAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3xBxFAoxof *b3xxBoFAfxo&#zx → †
A2B2C2132DEFGHI:                BxoFxfofx3(-x)(-x)(-x)ooofff3xBofFxxof *b3xxCxfFfxo&#zx → †
A2B2C2132DEF32GHI:              BxoFxFofx3(-x)(-x)(-x)oo(-x)fff3xBofFoxof *b3xxCxfAfxo&#zx → †
A2B2C2132DE12FGHI:              BxoFofofx3(-x)(-x)(-x)o(-x)offf3xBofAxxof *b3xxCxFFfxo&#zx → †
A2B2C2132DE12F32GHI:            BxoFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3xBofAoxof *b3xxCxFAfxo&#zx → †
A2B2C2132D42EFGHI:              BxoAxfofx3(-x)(-x)(-x)(-x)oofff3xBoFFxxof *b3xxCofFfxo&#zx → †
A2B2C2132D42EF32GHI:            BxoAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3xBoFFoxof *b3xxCofAfxo&#zx → †
A2B2C2132D42E12FGHI:            BxoAofofx3(-x)(-x)(-x)(-x)(-x)offf3xBoFAxxof *b3xxCoFFfxo&#zx → †
A2B2C2132D42E12F32GHI:          BxoAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3xBoFAoxof *b3xxCoFAfxo&#zx → †
A2B21C21DE12FGHI1:              B(-x)(-x)Fofof(-x)3(-x)ooo(-x)offF3xBxfAxxof *b3xxBxFFfxo&#zx → †
A2B21C21DE12F32GHI1:            B(-x)(-x)FoFof(-x)3(-x)ooo(-x)(-x)ffF3xBxfAoxof *b3xxBxFAfxo&#zx → †
A2B21C21D42E12FGHI1:            B(-x)(-x)Aofof(-x)3(-x)oo(-x)(-x)offF3xBxFAxxof *b3xxBoFFfxo&#zx → †
A2B21C21D42E12F32GHI1:          B(-x)(-x)AoFof(-x)3(-x)oo(-x)(-x)(-x)ffF3xBxFAoxof *b3xxBoFAfxo&#zx → †
A2B21C2132DE12FGHI1:            B(-x)oFofof(-x)3(-x)o(-x)o(-x)offF3xBofAxxof *b3xxCxFFfxo&#zx → †
A2B21C2132DE12F32GHI1:          B(-x)oFoFof(-x)3(-x)o(-x)o(-x)(-x)ffF3xBofAoxof *b3xxCxFAfxo&#zx → †
A2B21C2132D42E12FGHI1:          B(-x)oAofof(-x)3(-x)o(-x)(-x)(-x)offF3xBoFAxxof *b3xxCoFFfxo&#zx → †
A2B21C2132D42E12F32GHI1:        B(-x)oAoFof(-x)3(-x)o(-x)(-x)(-x)(-x)ffF3xBoFAoxof *b3xxCoFAfxo&#zx → †
A2B2142C2DEFGHI:                BoxFxfofx3(-x)(-x)(-x)ooofff3xCxfFxxof *b3xoBxfFfxo&#zx → †
A2B2142C2DEF32GHI:              BoxFxFofx3(-x)(-x)(-x)oo(-x)fff3xCxfFoxof *b3xoBxfAfxo&#zx → †
A2B2142C2DE12FGHI:              BoxFofofx3(-x)(-x)(-x)o(-x)offf3xCxfAxxof *b3xoBxFFfxo&#zx → †
A2B2142C2DE12F32GHI:            BoxFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3xCxfAoxof *b3xoBxFAfxo&#zx → †
A2B2142C2D42EFGHI:              BoxAxfofx3(-x)(-x)(-x)(-x)oofff3xCxFFxxof *b3xoBofFfxo&#zx → †
A2B2142C2D42EF32GHI:            BoxAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3xCxFFoxof *b3xoBofAfxo&#zx → †
A2B2142C2D42E12FGHI:            BoxAofofx3(-x)(-x)(-x)(-x)(-x)offf3xCxFAxxof *b3xoBoFFfxo&#zx → †
A2B2142C2D42E12F32GHI:          BoxAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3xCxFAoxof *b3xoBoFAfxo&#zx → †
A2B2142C21DE12FGHI1:            Bo(-x)Fofof(-x)3(-x)(-x)oo(-x)offF3xCxfAxxof *b3xoBxFFfxo&#zx → †
A2B2142C21DE12F32GHI1:          Bo(-x)FoFof(-x)3(-x)(-x)oo(-x)(-x)ffF3xCxfAoxof *b3xoBxFAfxo&#zx → †
A2B2142C21D42E12FGHI1:          Bo(-x)Aofof(-x)3(-x)(-x)o(-x)(-x)offF3xCxFAxxof *b3xoBoFFfxo&#zx → †
A2B2142C21D42E12F32GHI1:        Bo(-x)AoFof(-x)3(-x)(-x)o(-x)(-x)(-x)ffF3xCxFAoxof *b3xoBoFAfxo&#zx → †
A2B2142C2132DEFGHI:             BooFxfofx3(-x)(-x)(-x)ooofff3xCofFxxof *b3xoCxfFfxo&#zx → †
A2B2142C2132DEF32GHI:           BooFxFofx3(-x)(-x)(-x)oo(-x)fff3xCofFoxof *b3xoCxfAfxo&#zx → †
A2B2142C2132DE12FGHI:           BooFofofx3(-x)(-x)(-x)o(-x)offf3xCofAxxof *b3xoCxFFfxo&#zx → †
A2B2142C2132DE12FGHI1:          BooFofof(-x)3(-x)(-x)(-x)o(-x)offF3xCofAxxof *b3xoCxFFfxo&#zx → †
A2B2142C2132DE12F32GHI:         BooFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3xCofAoxof *b3xoCxFAfxo&#zx → †
A2B2142C2132DE12F32GHI1:        BooFoFof(-x)3(-x)(-x)(-x)o(-x)(-x)ffF3xCofAoxof *b3xoCxFAfxo&#zx → †
A2B2142C2132D42EFGHI:           BooAxfofx3(-x)(-x)(-x)(-x)oofff3xCoFFxxof *b3xoCofFfxo&#zx → †
A2B2142C2132D42EF32GHI:         BooAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3xCoFFoxof *b3xoCofAfxo&#zx → †
A2B2142C2132D42E12FGHI:         BooAofofx3(-x)(-x)(-x)(-x)(-x)offf3xCoFAxxof *b3xoCoFFfxo&#zx → †
A2B2142C2132D42E12FGHI1:        BooAofof(-x)3(-x)(-x)(-x)(-x)(-x)offF3xCoFAxxof *b3xoCoFFfxo&#zx → †
A2B2142C2132D42E12F32GHI:       BooAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3xCoFAoxof *b3xoCoFAfxo&#zx → †
A2B2142C2132D42E12F32GHI1:      BooAoFof(-x)3(-x)(-x)(-x)(-x)(-x)(-x)ffF3xCoFAoxof *b3xoCoFAfxo&#zx → †
A23BC213DE1F3G3HI1:             Bo(-x)F(-x)fof(-x)3oxxxoxFfF3(-x)V(-x)fF(-x)(-x)of *b3xoBxfFfxo&#zx → †
A23B2C2132DEF32G3HI:            BxoFxFofx3o(-x)(-x)oo(-x)Fff3(-x)BofFo(-x)of *b3xxCxfAfxo&#zx → †
A23B2C2132DE12F32G3HI:          BxoFoFofx3o(-x)(-x)o(-x)(-x)Fff3(-x)BofAo(-x)of *b3xxCxFAfxo&#zx → †
A23B2C2132D42EF32G3HI:          BxoAxFofx3o(-x)(-x)(-x)o(-x)Fff3(-x)BoFFo(-x)of *b3xxCofAfxo&#zx → †
A23B2C2132D42E12F32G3HI:        BxoAoFofx3o(-x)(-x)(-x)(-x)(-x)Fff3(-x)BoFAo(-x)of *b3xxCoFAfxo&#zx → †
A23B21C213DE1F3G3HI1:           B(-x)(-x)F(-x)fof(-x)3ooxoxxFfF3(-x)B(-x)fF(-x)(-x)of *b3xxBxfFfxo&#zx → †
A23B21C2132DE12F32G3HI1:        B(-x)oFoFof(-x)3oo(-x)o(-x)(-x)FfF3(-x)BofAo(-x)of *b3xxCxFAfxo&#zx → †
A23B21C2132D42E12F32G3HI1:      B(-x)oAoFof(-x)3oo(-x)(-x)(-x)(-x)FfF3(-x)BoFAo(-x)of *b3xxCoFAfxo&#zx → †
A23B2142C2132DEF32G3HI:         BooFxFofx3o(-x)(-x)oo(-x)Fff3(-x)CofFo(-x)of *b3xoCxfAfxo&#zx → †
A23B2142C2132DE12F32G3HI:       BooFoFofx3o(-x)(-x)o(-x)(-x)Fff3(-x)CofAo(-x)of *b3xoCxFAfxo&#zx → †
A23B2142C2132DE12F32G3HI1:      BooFoFof(-x)3o(-x)(-x)o(-x)(-x)FfF3(-x)CofAo(-x)of *b3xoCxFAfxo&#zx → †
A23B2142C2132D42EF32G3HI:       BooAxFofx3o(-x)(-x)(-x)o(-x)Fff3(-x)CoFFo(-x)of *b3xoCofAfxo&#zx → †
A23B2142C2132D42E12F32G3HI:     BooAoFofx3o(-x)(-x)(-x)(-x)(-x)Fff3(-x)CoFAo(-x)of *b3xoCoFAfxo&#zx → †
A23B2142C2132D42E12F32G3HI1:    BooAoFof(-x)3o(-x)(-x)(-x)(-x)(-x)FfF3(-x)CoFAo(-x)of *b3xoCoFAfxo&#zx → †
A23B2142C23DEF32G3HI:           BoxFxFofx3o(-x)ooo(-x)Fff3(-x)C(-x)fFo(-x)of *b3xoBxfAfxo&#zx → †
A23B2142C23DE12F32G3HI:         BoxFoFofx3o(-x)oo(-x)(-x)Fff3(-x)C(-x)fAo(-x)of *b3xoBxFAfxo&#zx → †
A23B2142C23D42EF32G3HI:         BoxAxFofx3o(-x)o(-x)o(-x)Fff3(-x)C(-x)FFo(-x)of *b3xoBofAfxo&#zx → †
A23B2142C23D42E12F32G3HI:       BoxAoFofx3o(-x)o(-x)(-x)(-x)Fff3(-x)C(-x)FAo(-x)of *b3xoBoFAfxo&#zx → †
A234BC213D4E1F3G3H4I1:          Bo(-x)F(-x)fof(-x)3xxxxxxFFF3(-x)V(-x)fF(-x)(-x)of *b3(-x)oB(-x)fFf(-x)o&#zx → †
A234B214CD4E1F3G3H4I1:          B(-x)oF(-x)fof(-x)3xxxxxxFFF3(-x)BofF(-x)(-x)of *b3(-x)(-x)V(-x)fFf(-x)o&#zx → †
A234B214C213D4E1F3G3H4I1:       B(-x)(-x)F(-x)fof(-x)3xxxxxxFFF3(-x)B(-x)fF(-x)(-x)of *b3(-x)(-x)B(-x)fFf(-x)o&#zx → †
A2342B2C2132DEFGHI:             CxoFxfofx3(-x)(-x)(-x)ooofff3oBofFxxof *b3oxCxfFfxo&#zx → †
A2342B2C2132DEF32GHI:           CxoFxFofx3(-x)(-x)(-x)oo(-x)fff3oBofFoxof *b3oxCxfAfxo&#zx → †
A2342B2C2132DEF32G3HI:          CxoFxFofx3(-x)(-x)(-x)oo(-x)Fff3oBofFo(-x)of *b3oxCxfAfxo&#zx → †
A2342B2C2132DE12FGHI:           CxoFofofx3(-x)(-x)(-x)o(-x)offf3oBofAxxof *b3oxCxFFfxo&#zx → †
A2342B2C2132DE12F32GHI:         CxoFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3oBofAoxof *b3oxCxFAfxo&#zx → †
A2342B2C2132DE12F32G3HI:        CxoFoFofx3(-x)(-x)(-x)o(-x)(-x)Fff3oBofAo(-x)of *b3oxCxFAfxo&#zx → †
A2342B2C2132D42EFGHI:           CxoAxfofx3(-x)(-x)(-x)(-x)oofff3oBoFFxxof *b3oxCofFfxo&#zx → †
A2342B2C2132D42EF32GHI:         CxoAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3oBoFFoxof *b3oxCofAfxo&#zx → †
A2342B2C2132D42EF32G3HI:        CxoAxFofx3(-x)(-x)(-x)(-x)o(-x)Fff3oBoFFo(-x)of *b3oxCofAfxo&#zx → †
A2342B2C2132D42E12FGHI:         CxoAofofx3(-x)(-x)(-x)(-x)(-x)offf3oBoFAxxof *b3oxCoFFfxo&#zx → †
A2342B2C2132D42E12F32GHI:       CxoAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3oBoFAoxof *b3oxCoFAfxo&#zx → †
A2342B2C2132D42E12F32G3HI:      CxoAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)Fff3oBoFAo(-x)of *b3oxCoFAfxo&#zx → †
A2342B21C21DE12FGHI1:           C(-x)(-x)Fofof(-x)3(-x)ooo(-x)offF3oBxfAxxof *b3oxBxFFfxo&#zx → †
A2342B21C21DE12F32GHI1:         C(-x)(-x)FoFof(-x)3(-x)ooo(-x)(-x)ffF3oBxfAoxof *b3oxBxFAfxo&#zx → †
A2342B21C21D42E12FGHI1:         C(-x)(-x)Aofof(-x)3(-x)oo(-x)(-x)offF3oBxFAxxof *b3oxBoFFfxo&#zx → †
A2342B21C21D42E12F32GHI1:       C(-x)(-x)AoFof(-x)3(-x)oo(-x)(-x)(-x)ffF3oBxFAoxof *b3oxBoFAfxo&#zx → †
A2342B21C2132DE12FGHI1:         C(-x)oFofof(-x)3(-x)o(-x)o(-x)offF3oBofAxxof *b3oxCxFFfxo&#zx → †
A2342B21C2132DE12F32GHI1:       C(-x)oFoFof(-x)3(-x)o(-x)o(-x)(-x)ffF3oBofAoxof *b3oxCxFAfxo&#zx → †
A2342B21C2132DE12F32G3HI1:      C(-x)oFoFof(-x)3(-x)o(-x)o(-x)(-x)FfF3oBofAo(-x)of *b3oxCxFAfxo&#zx → †
A2342B21C2132D42E12FGHI1:       C(-x)oAofof(-x)3(-x)o(-x)(-x)(-x)offF3oBoFAxxof *b3oxCoFFfxo&#zx → †
A2342B21C2132D42E12F32GHI1:     C(-x)oAoFof(-x)3(-x)o(-x)(-x)(-x)(-x)ffF3oBoFAoxof *b3oxCoFAfxo&#zx → †
A2342B21C2132D42E12F32G3HI1:    C(-x)oAoFof(-x)3(-x)o(-x)(-x)(-x)(-x)FfF3oBoFAo(-x)of *b3oxCoFAfxo&#zx → †
A2342B2142C2DEFGHI:             CoxFxfofx3(-x)(-x)(-x)ooofff3oCxfFxxof *b3ooBxfFfxo&#zx → †
A2342B2142C2DEF32GHI:           CoxFxFofx3(-x)(-x)(-x)oo(-x)fff3oCxfFoxof *b3ooBxfAfxo&#zx → †
A2342B2142C2DE12FGHI:           CoxFofofx3(-x)(-x)(-x)o(-x)offf3oCxfAxxof *b3ooBxFFfxo&#zx → †
A2342B2142C2DE12F32GHI:         CoxFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3oCxfAoxof *b3ooBxFAfxo&#zx → †
A2342B2142C2D42EFGHI:           CoxAxfofx3(-x)(-x)(-x)(-x)oofff3oCxFFxxof *b3ooBofFfxo&#zx → †
A2342B2142C2D42EFGH4I:          CoxAxfofx3(-x)(-x)(-x)(-x)oofFf3oCxFFxxof *b3ooBofFf(-x)o&#zx → †
A2342B2142C2D42EF32GHI:         CoxAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3oCxFFoxof *b3ooBofAfxo&#zx → †
A2342B2142C2D42EF32GH4I:        CoxAxFofx3(-x)(-x)(-x)(-x)o(-x)fFf3oCxFFoxof *b3ooBofAf(-x)o&#zx → †
A2342B2142C2D42E12FGHI:         CoxAofofx3(-x)(-x)(-x)(-x)(-x)offf3oCxFAxxof *b3ooBoFFfxo&#zx → †
A2342B2142C2D42E12FGH4I:        CoxAofofx3(-x)(-x)(-x)(-x)(-x)ofFf3oCxFAxxof *b3ooBoFFf(-x)o&#zx → †
A2342B2142C2D42E12F32GHI:       CoxAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3oCxFAoxof *b3ooBoFAfxo&#zx → †
A2342B2142C2D42E12F32GH4I:      CoxAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fFf3oCxFAoxof *b3ooBoFAf(-x)o&#zx → †
A2342B2142C21DE12FGHI1:         Co(-x)Fofof(-x)3(-x)(-x)oo(-x)offF3oCxfAxxof *b3ooBxFFfxo&#zx → †
A2342B2142C21DE12F32GHI1:       Co(-x)FoFof(-x)3(-x)(-x)oo(-x)(-x)ffF3oCxfAoxof *b3ooBxFAfxo&#zx → †
A2342B2142C21D42E12FGHI1:       Co(-x)Aofof(-x)3(-x)(-x)o(-x)(-x)offF3oCxFAxxof *b3ooBoFFfxo&#zx → †
A2342B2142C21D42E12FGH4I1:      Co(-x)Aofof(-x)3(-x)(-x)o(-x)(-x)ofFF3oCxFAxxof *b3ooBoFFf(-x)o&#zx → †
A2342B2142C21D42E12F32GHI1:     Co(-x)AoFof(-x)3(-x)(-x)o(-x)(-x)(-x)ffF3oCxFAoxof *b3ooBoFAfxo&#zx → †
A2342B2142C21D42E12F32GH4I1:    Co(-x)AoFof(-x)3(-x)(-x)o(-x)(-x)(-x)fFF3oCxFAoxof *b3ooBoFAf(-x)o&#zx → †
A2342B2142C2132DEFGHI:          CooFxfofx3(-x)(-x)(-x)ooofff3oCofFxxof *b3ooCxfFfxo&#zx → †
A2342B2142C2132DEF32GHI:        CooFxFofx3(-x)(-x)(-x)oo(-x)fff3oCofFoxof *b3ooCxfAfxo&#zx → †
A2342B2142C2132DEF32G3HI:       CooFxFofx3(-x)(-x)(-x)oo(-x)Fff3oCofFo(-x)of *b3ooCxfAfxo&#zx → †
A2342B2142C2132DE12FGHI:        CooFofofx3(-x)(-x)(-x)o(-x)offf3oCofAxxof *b3ooCxFFfxo&#zx → †
A2342B2142C2132DE12FGHI1:       CooFofof(-x)3(-x)(-x)(-x)o(-x)offF3oCofAxxof *b3ooCxFFfxo&#zx → †
A2342B2142C2132DE12F32GHI:      CooFoFofx3(-x)(-x)(-x)o(-x)(-x)fff3oCofAoxof *b3ooCxFAfxo&#zx → †
A2342B2142C2132DE12F32GHI1:     CooFoFof(-x)3(-x)(-x)(-x)o(-x)(-x)ffF3oCofAoxof *b3ooCxFAfxo&#zx → †
A2342B2142C2132DE12F32G3HI:     CooFoFofx3(-x)(-x)(-x)o(-x)(-x)Fff3oCofAo(-x)of *b3ooCxFAfxo&#zx → †
A2342B2142C2132DE12F32G3HI1:    CooFoFof(-x)3(-x)(-x)(-x)o(-x)(-x)FfF3oCofAo(-x)of *b3ooCxFAfxo&#zx → †
A2342B2142C2132D42EFGHI:        CooAxfofx3(-x)(-x)(-x)(-x)oofff3oCoFFxxof *b3ooCofFfxo&#zx → †
A2342B2142C2132D42EFGH4I:       CooAxfofx3(-x)(-x)(-x)(-x)oofFf3oCoFFxxof *b3ooCofFf(-x)o&#zx → †
A2342B2142C2132D42EF32GHI:      CooAxFofx3(-x)(-x)(-x)(-x)o(-x)fff3oCoFFoxof *b3ooCofAfxo&#zx → †
A2342B2142C2132D42EF32GH4I:     CooAxFofx3(-x)(-x)(-x)(-x)o(-x)fFf3oCoFFoxof *b3ooCofAf(-x)o&#zx → †
A2342B2142C2132D42EF32G3HI:     CooAxFofx3(-x)(-x)(-x)(-x)o(-x)Fff3oCoFFo(-x)of *b3ooCofAfxo&#zx → †
A2342B2142C2132D42EF32G3H4I:    CooAxFofx3(-x)(-x)(-x)(-x)o(-x)FFf3oCoFFo(-x)of *b3ooCofAf(-x)o&#zx → †
A2342B2142C2132D42E12FGHI:      CooAofofx3(-x)(-x)(-x)(-x)(-x)offf3oCoFAxxof *b3ooCoFFfxo&#zx → †
A2342B2142C2132D42E12FGHI1:     CooAofof(-x)3(-x)(-x)(-x)(-x)(-x)offF3oCoFAxxof *b3ooCoFFfxo&#zx → †
A2342B2142C2132D42E12FGH4I:     CooAofofx3(-x)(-x)(-x)(-x)(-x)ofFf3oCoFAxxof *b3ooCoFFf(-x)o&#zx → †
A2342B2142C2132D42E12FGH4I1:    CooAofof(-x)3(-x)(-x)(-x)(-x)(-x)ofFF3oCoFAxxof *b3ooCoFFf(-x)o&#zx → †
A2342B2142C2132D42E12F32GHI:    CooAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fff3oCoFAoxof *b3ooCoFAfxo&#zx → †
A2342B2142C2132D42E12F32GHI1:   CooAoFof(-x)3(-x)(-x)(-x)(-x)(-x)(-x)ffF3oCoFAoxof *b3ooCoFAfxo&#zx → †
A2342B2142C2132D42E12F32GH4I:   CooAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)fFf3oCoFAoxof *b3ooCoFAf(-x)o&#zx → †
A2342B2142C2132D42E12F32GH4I1:  CooAoFof(-x)3(-x)(-x)(-x)(-x)(-x)(-x)fFF3oCoFAoxof *b3ooCoFAf(-x)o&#zx → †
A2342B2142C2132D42E12F32G3HI:   CooAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)Fff3oCoFAo(-x)of *b3ooCoFAfxo&#zx → †
A2342B2142C2132D42E12F32G3HI1:  CooAoFof(-x)3(-x)(-x)(-x)(-x)(-x)(-x)FfF3oCoFAo(-x)of *b3ooCoFAfxo&#zx → †
A2342B2142C2132D42E12F32G3H4I:  CooAoFofx3(-x)(-x)(-x)(-x)(-x)(-x)FFf3oCoFAo(-x)of *b3ooCoFAf(-x)o&#zx → †
A2342B2142C2132D42E12F32G3H4I1: CooAoFof(-x)3(-x)(-x)(-x)(-x)(-x)(-x)FFF3oCoFAo(-x)of *b3ooCoFAf(-x)o&#zx → †
A2342B2142C23DEF32G3HI:         CoxFxFofx3(-x)(-x)ooo(-x)Fff3oC(-x)fFo(-x)of *b3ooBxfAfxo&#zx → †
A2342B2142C23DE12F32G3HI:       CoxFoFofx3(-x)(-x)oo(-x)(-x)Fff3oC(-x)fAo(-x)of *b3ooBxFAfxo&#zx → †
A2342B2142C23D42EF32G3HI:       CoxAxFofx3(-x)(-x)o(-x)o(-x)Fff3oC(-x)FFo(-x)of *b3ooBofAfxo&#zx → †
A2342B2142C23D42EF32G3H4I:      CoxAxFofx3(-x)(-x)o(-x)o(-x)FFf3oC(-x)FFo(-x)of *b3ooBofAf(-x)o&#zx → †
A2342B2142C23D42E12F32G3HI:     CoxAoFofx3(-x)(-x)o(-x)(-x)(-x)Fff3oC(-x)FAo(-x)of *b3ooBoFAfxo&#zx → †
A2342B2142C23D42E12F32G3H4I:    CoxAoFofx3(-x)(-x)o(-x)(-x)(-x)FFf3oC(-x)FAo(-x)of *b3ooBoFAf(-x)o&#zx → †
A2342B24C2132D42EFGH4I:         CxoAxfofx3(-x)o(-x)(-x)oofFf3oBoFFxxof *b3o(-x)CofFf(-x)o&#zx → †
A2342B24C2132D42EF32GH4I:       CxoAxFofx3(-x)o(-x)(-x)o(-x)fFf3oBoFFoxof *b3o(-x)CofAf(-x)o&#zx → †
A2342B24C2132D42EF32G3H4I:      CxoAxFofx3(-x)o(-x)(-x)o(-x)FFf3oBoFFo(-x)of *b3o(-x)CofAf(-x)o&#zx → †
A2342B24C2132D42E12FGH4I:       CxoAofofx3(-x)o(-x)(-x)(-x)ofFf3oBoFAxxof *b3o(-x)CoFFf(-x)o&#zx → †
A2342B24C2132D42E12F32GH4I:     CxoAoFofx3(-x)o(-x)(-x)(-x)(-x)fFf3oBoFAoxof *b3o(-x)CoFAf(-x)o&#zx → †
A2342B24C2132D42E12F32G3H4I:    CxoAoFofx3(-x)o(-x)(-x)(-x)(-x)FFf3oBoFAo(-x)of *b3o(-x)CoFAf(-x)o&#zx → †
A24B214CD4E1FGH4I1:             B(-x)oF(-x)fof(-x)3oxxxxofFF3xBofFxxof *b3(-x)(-x)V(-x)fFf(-x)o&#zx → †
A24B214C21D4E1FGH4I1:           B(-x)(-x)F(-x)fof(-x)3oxoxxofFF3xBxfFxxof *b3(-x)(-x)B(-x)fFf(-x)o&#zx → †
A24B2142C2D42EFGH4I:            BoxAxfofx3o(-x)(-x)(-x)oofFf3xCxFFxxof *b3(-x)oBofFf(-x)o&#zx → †
A24B2142C2D42EF32GH4I:          BoxAxFofx3o(-x)(-x)(-x)o(-x)fFf3xCxFFoxof *b3(-x)oBofAf(-x)o&#zx → †
A24B2142C2D42E12FGH4I:          BoxAofofx3o(-x)(-x)(-x)(-x)ofFf3xCxFAxxof *b3(-x)oBoFFf(-x)o&#zx → †
A24B2142C2D42E12F32GH4I:        BoxAoFofx3o(-x)(-x)(-x)(-x)(-x)fFf3xCxFAoxof *b3(-x)oBoFAf(-x)o&#zx → †
A24B2142C21D42E12FGH4I1:        Bo(-x)Aofof(-x)3o(-x)o(-x)(-x)ofFF3xCxFAxxof *b3(-x)oBoFFf(-x)o&#zx → †
A24B2142C21D42E12F32GH4I1:      Bo(-x)AoFof(-x)3o(-x)o(-x)(-x)(-x)fFF3xCxFAoxof *b3(-x)oBoFAf(-x)o&#zx → †
A24B2142C2132D42EFGH4I:         BooAxfofx3o(-x)(-x)(-x)oofFf3xCoFFxxof *b3(-x)oCofFf(-x)o&#zx → †
A24B2142C2132D42EF32GH4I:       BooAxFofx3o(-x)(-x)(-x)o(-x)fFf3xCoFFoxof *b3(-x)oCofAf(-x)o&#zx → †
A24B2142C2132D42E12FGH4I:       BooAofofx3o(-x)(-x)(-x)(-x)ofFf3xCoFAxxof *b3(-x)oCoFFf(-x)o&#zx → †
A24B2142C2132D42E12FGH4I1:      BooAofof(-x)3o(-x)(-x)(-x)(-x)ofFF3xCoFAxxof *b3(-x)oCoFFf(-x)o&#zx → †
A24B2142C2132D42E12F32GH4I:     BooAoFofx3o(-x)(-x)(-x)(-x)(-x)fFf3xCoFAoxof *b3(-x)oCoFAf(-x)o&#zx → †
A24B2142C2132D42E12F32GH4I1:    BooAoFof(-x)3o(-x)(-x)(-x)(-x)(-x)fFF3xCoFAoxof *b3(-x)oCoFAf(-x)o&#zx → †
Stott expansion:
(derived CRFs)
2:A2B2C2DEFGHI: Bxx|Fxf|ofx 3 ooo|xxx|FFF 3 xBx|fFx|xof *b3 xxB|xfF|fxo &#zx
  → CRF with cell list:
        24  coes
        24  ikes
        192 oct
        144 pip
        288 squippies (J1)
        96  thawroes (J92)
        96  tricues (J3)
        96  trip
using here node marks / (pseudo) edge lengths: F=f+x=ff, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x=fff, C=2F=2f+2x, R=A+x=f+3x, S=C+x=2f+3x

in o5o2o5o subsymmetry   (up)
Representation:
Aooo|Fxox|Vofo|Fofx|xf 5 oAoo|xFxo|oVof|oFxf|xf 2 ooAo|xoFx|ofVo|xfFo|fx 5 oooA|oxxF|fooV|fxoF|fx &#zx  (rox)

with cyclical layer symmetries: A(1234) → B(2143) → C(4312) → D(3421) → A(1234)
                                E(1234) → F(2143) → G(4312) → H(3421) → E(1234)
                                I(1234) → J(2143) → K(4312) → L(3421) → I(1234)
                                M(1234) → N(2143) → O(4312) → P(3421) → M(1234)
                                Q(1234) → Q(2143) → R(4312) → R(3421) → Q(1234)
All layers &
kaleido-facetings per layer:
A: A5o o5o
B: o5A o5o
C: o5o A5o
D: o5o o5A

E: F5x x5o  → E2: B5(-x) x5o  → E23: B5(-x) (-x)5f
            ↳ E3: F5x (-x)5f
F: x5F o5x  → F1: (-x)5B o5x  → F14: (-x)5B f5(-x)
            ↳ F4: x5F f5(-x)
G: o5x F5x  → G2: f5(-x) F5x  → G24: f5(-x) B5(-x)
            ↳ G4: o5x B5(-x)
H: x5o x5F  → H1: (-x)5f x5F  → H13: (-x)5f (-x)5B
            ↳ H3: x5o (-x)5B
I: V5o o5f
J: o5V f5o
K: f5o V5o
L: o5f o5V

M: F5o x5f  → M3: F5o (-x)5V
N: o5F f5x  → N4: o5F V5(-x)
O: f5x F5o  → O2: V5(-x) F5o
P: x5f o5F  → P1: (-x)5V o5F

Q: x5x f5f  → Q1: (-x)5F f5f
            ↳ Q2: F5(-x) f5f
R: f5f x5x  → R3: f5f (-x)5F
            ↳ R4: f5f F5(-x)
A priori invalid combinations:
E   + G2,G24,H3,H13,M3,O2,Q2,R3
E2  + G,G4,H3,H13,M3,O,Q,R3
E3  + G2,G24,H,H1,M,O2,Q2,R
E23 + G,G4,H,H1,M,O,Q,R
F   + G4,G24,H1,H13,N4,P1,Q1,R4
F1  + G4,G24,H,H3,N4,P,Q,R4
F4  + G,G2,H1,H13,N,P1,Q1,R
F14 + G,G2,H,H3,N,P,Q,R
G   + N4,O2,Q2,R4
G2  + N4,O,Q,R4
G4  + N,O2,Q2,R
G24 + N,O,Q,R
H   + M3,P1,Q1,R3
H1  + M3,P,Q,R3
H3  + M,P1,Q1,R
H13 + M,P,Q,R
M   + R3
M3  + R
N   + R4
N4  + R
O   + Q2
O2  + Q
P   + Q1
P1  + Q
Other layer-combinations:
E2F1G2H1MNO2P1Q1R:        AoooB(-x)f(-x)VofoFoV(-x)(-x)f 5 oAoo(-x)B(-x)foVofoF(-x)VFf 2 ooAoxoFxofVoxfFofx 5 oooAoxxFfooVfxoFfx &#zx
E23F14G24H13M3N4O2P1Q1R3: AoooB(-x)f(-x)VofoFoV(-x)(-x)f 5 oAoo(-x)B(-x)foVofoF(-x)VFf 2 ooAo(-x)fB(-x)ofVo(-x)VFof(-x) 5 oooAf(-x)(-x)BfooVV(-x)oFfF &#zx
Stott expansion:
(derived potential CRFs)
12:E2F1G2H1MNO2P1Q1R: RxxxCoFoBxFxAxBooF 5 xRxxoCoFxBxFxAoBAF 2 ooAoxoFxofVoxfFofx 5 oooAoxxFfooVfxoFfx &#zx → ‡ (F in G)
1234:E23F14G24H13M3N4O2P1Q1R3: RxxxCoFoBxFxAxBooF 5 xRxxoCoFxBxFxAoBAF 2 xxRxoFCoxFBxoBAxFo 5 xxxRFooCFxxBBoxAFA &#zx → ‡ (F in G)
using here node marks / (pseudo) edge lengths: F=f+x=ff, V=F+v=2f, A=F+x=f+2x, B=V+x=2f+x=fff, C=2F=2f+2x, R=A+x=f+3x


EKF of the small prismated icositetrachoron (x3o4o3x)

©

in o2o3o4o subsymmetry   (up)
Representation:
oxqwQ 2 qowxx 3 xxooo 4 oxoxo &#zx  (spic)
All layers &
kaleido-facetings per layer:
A: o2q3x4o  → A3: o2w3(-x)4q
B: x2o3x4x  → B1: (-x)2o3x4x  → B13: (-x)2x3(-x)4w  → B132: (-x)2(-x)3o4w
                              ↳ B14: (-x)2o3w4(-x)
            ↳ B3: x2x3(-x)4w  → (B31 = B13)
                              ↳ B32: x2(-x)3o4w     → (B321 = B132)
            ↳ B4: x2o3w4(-x)  → (B41 = B14)
C: q2w3o4o
D: w2x3o4x  → D2: w2(-x)3x4x  → D23: w2o3(-x)4w
                              ↳ D24: w2(-x)3w4(-x)
            ↳ D4: w2x3q4(-x)  → (D42 = D24)
E: Q2x3o4o  → E2: Q2(-x)3x4o  → E23: Q2o3(-x)4q
A priori invalid combinations:
A    + B3,B13,D23,E23
A3   + B,B1,D2,E2
B    + D4,D23,D24,E23
B1   + D4,D23,D24,E23
B3   + D2,D24,E2
B4   + D,D2
B13  + D2,D24,E2
B14  + D,D2
B32  + D,D4,E
B132 + D,D4,E
D    + E2
D2   + E,E23
D4   + E2
D23  + E2
D24  + E   (all giving rise to u edges)

E23   (giving rise to q or w edges within extremal layer)
Other layer-combinations:
ABCD2E2        oxqwQ 2 qow(-x)(-x) 3 xxoxx 4 oxoxo &#zx  → ‡ (dead end at C)
AB1CDE         o(-x)qwQ 2 qowxx 3 xxooo 4 oxoxo &#zx  → ‡ (q in A)
AB1CD2E2       o(-x)qwQ 2 qow(-x)(-x) 3 xxoxx 4 oxoxo &#zx  → †
AB4CD4E        oxqwQ 2 qowxx 3 xwoqo 4 o(-x)o(-x)o &#zx  → ‡ (q in A)
AB4CD24E2      oxqwQ 2 qow(-x)(-x) 3 xwowx 4 o(-x)o(-x)o &#zx  → ‡ (dead end at C)
AB14CD4E       o(-x)qwQ 2 qowxx 3 xwoqo 4 o(-x)o(-x)o &#zx  → ‡ (w in B)
AB14CD24E2     o(-x)qwQ 2 qow(-x)(-x) 3 xwowx 4 o(-x)o(-x)o &#zx  → †
AB32CD2E2      oxqwQ 2 q(-x)w(-x)(-x) 3 xooxx 4 owoxo &#zx  → †
AB32CD24E2     oxqwQ 2 q(-x)w(-x)(-x) 3 xoowx 4 owo(-x)o &#zx  → †
AB132CD24E2    o(-x)qwQ 2 q(-x)w(-x)(-x) 3 xoowx 4 owo(-x)o &#zx  → †
A3B3CDE        oxqwQ 2 wxwxx 3 (-x)(-x)ooo 4 qwoxo &#zx
A3B3CD4E       oxqwQ 2 wxwxx 3 (-x)(-x)oqo 4 qwo(-x)o &#zx  → ‡ (dead end at B)
A3B3CD23E      oxqwQ 2 wxwox 3 (-x)(-x)o(-x)o 4 qwowo &#zx  → †
A3B4CD4E       oxqwQ 2 wowxx 3 (-x)woqo 4 q(-x)o(-x)o &#zx  → ‡ (w in C)
A3B4CD23E      oxqwQ 2 wowox 3 (-x)wo(-x)o 4 q(-x)owo &#zx  → †
A3B13CDE       o(-x)qwQ 2 wxwxx 3 (-x)(-x)ooo 4 qwoxo &#zx  → ‡ (w in C)
A3B13CD4E      o(-x)qwQ 2 wxwxx 3 (-x)(-x)oqo 4 qwo(-x)o &#zx  → ‡ (w in D)
A3B13CD23E     o(-x)qwQ 2 wxwox 3 (-x)(-x)o(-x)o 4 qwowo &#zx  → †
A3B14CD4E      o(-x)qwQ 2 wowxx 3 (-x)woqo 4 q(-x)o(-x)o &#zx  → †
A3B14CD23E     o(-x)qwQ 2 wowox 3 (-x)wo(-x)o 4 q(-x)owo &#zx  → †
Stott expansion:
(derived CRFs)
3:A3B3CDE: oxqwQ 2 wxwxx 3 ooxxx 4 qwoxo &#zx
  → CRF with cell list:
        6  coes
        16 hips
        12 sircoes
        12 squobcues (J28)
        2  toes
        16 tricues (J3)
        80 trips

related: oxqw. 2 wxwx. 3 ooxx. 4 qwox. &#zx
  → CRF with cell list:
        6  coes
        2  gircoes
        12 sircoes
        12 squacues (J4)
        16 tricues (J3)
        56 trips
using here node marks / (pseudo) edge lengths: Q=w+x=q+u, W=Q+x=w+u
in . o3o4o subsymmetry   (up)
additional,
not prismatically symmetric
combinations of formers:
none 

in o3o3o *b3o subsymmetry   (up)
Representation:
qoo 3 xxx 3 oqo *b3ooq &#zx  (spic)

with layer cycle:  A(134) → B(341) → C(413) → A(134)
All layers &
kaleido-facetings per layer:
A: q3x3o *b3o  →  A2: w3(-x)3x *b3x  →  A23: w3o3(-x) *b3x  →  A234: w3x3(-x) *b3(-x)  →  A2342: Q3(-x)3o *b3o
                                     ↳  A24: w3o3x *b3(-x)  →  (A243 = A234)           →  (A2432 = A2342)
B: o3x3q *b3o  →  B2: x3(-x)3w *b3x  →  B21: (-x)3o3w *b3x  →  B214: (-x)3x3w *b3(-x)  →  B2142: o3(-x)3Q *b3o
                                     ↳  B24: x3o3w *b3(-x)  →  (B241 = B214)           →  (B2412 = B2142)
C: o3x3o *b3q  →  C2: x3(-x)3x *b3w  →  C21: (-x)3o3x *b3w  →  C213: (-x)3x3(-x) *b3w  →  C2132: o3(-x)3o *b3Q
                                     ↳  C23: x3o3(-x) *b3w  →  (C231 = C213)           →  (C2312 = C2132)
A priori invalid combinations:
A     + B2,B2142,C2,C2132
A2    + B,B24,B214,C,C23,C213
A23   + B24,B214,C2,C21
A24   + B21,C2,C23,C213
A234  + B2,B21,B2142,C2,C21,C2132
A2342 + B,B214,C,C213
B     + C2,C213
B2    + C,C21,C213
B21   + C2,C23
B24   + C21,C213
B214  + C2,C23,C2132
B2142 + C,C213
Other layer-combinations:
ABC21           qo(-x) 3 xxo 3 oqx *b3 oow &#zx  → †
ABC23           qox 3 xxo 3 oq(-x) *b3 oow &#zx  → †
AB21C21         q(-x)(-x) 3 xoo 3 owx *b3 oxw &#zx  → †
AB21C213        q(-x)(-x) 3 xox 3 ow(-x) *b3 oxw &#zx  → †
AB24C23         qxx 3 xoo 3 ow(-x) *b3 o(-x)w &#zx  → †
AB214C21        q(-x)(-x) 3 xxo 3 owx *b3 o(-x)w &#zx  → †
AB214C213       q(-x)(-x) 3 xxx 3 ow(-x) *b3 o(-x)w &#zx  → †
A2B2C2          wxx 3 (-x)(-x)(-x) 3 xwx *b3 xxw &#zx
A2B2C2132       wxo 3 (-x)(-x)(-x) 3 xwo *b3 xxQ &#zx  → †
A2B21C21        w(-x)(-x) 3 (-x)oo 3 xwx *b3 xxw &#zx  → †
A2B21C2132      w(-x)o 3 (-x)o(-x) 3 xwo *b3 xxQ &#zx  → †
A2B2142C21      wo(-x) 3 (-x)(-x)o 3 xQx *b3 xow &#zx  → †
A2B2142C2132    woo 3 ( -x)(-x)(-x) 3 xQo *b3 xoQ &#zx  → †
A23B21C213      w(-x)(-x) 3 oox 3 (-x)w(-x) *b3 xxw &#zx  → †
A23B21C2132     w(-x)o 3 oo(-x) 3 (-x)wo *b3 xxQ &#zx  → †
A23B2142C23     wox 3 o(-x)o 3 (-x)Q(-x) *b3 xow &#zx  → †
A23B2142C2132   woo 3 o(-x)(-x) 3 (-x)Qo *b3 xoQ &#zx  → †
A24B2142C2132   woo 3 o(-x)(-x) 3 xQo *b3 (-x)oQ &#zx  → †
A234B214C213    w(-x)(-x) 3 xxx 3 (-x)w(-x) *b3 (-x)(-x)w &#zx  → †
A2342B2142C2132 Qoo 3 (-x)(-x)(-x) 3 oQo *b3 ooQ &#zx  → †
Stott expansion:
(derived CRFs)
1:ABC wxx 3 xxx 3 oqo *b3 ooq &#zx
  → CRF with cell list:
        24  esquidpies (J15)
        32  hips
        8   octs
        160 trips
        16  tuts

related: .xx 3 .xx 3 .qo *b3 .oq &#zx
   = Wythoffian x3x3o4x (prit) with cell list:
        24 cubes
        32 hips
        8  sircoes
        16 tuts
(-2):ABC qoo 3 ooo 3 oqo *b3 ooq &#zx
  = Wythoffian x3o4o3o (ico) with cell list:
        24 octs

related: .oo 3 .oo 3 .qo *b3 .oq &#zx
  = Wythoffian o3o3o4x (tes) with cell list:
        8 cubes
1(-2):ABC wxx 3 ooo 3 oqo *b3 ooq &#zx
  → CRF with cell list:
        24 esquidpies (J15)
        16 tets
        32 trips

related: .xx 3 .oo 3 .qo *b3 .oq &#zx
   = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips
13:ABC wxx 3 xxx 3 xwx *b3 ooq &#zx
  → CRF with cell list:
        64  hips
        24  squobcues (J28)
        8   toes
        128 trips
        16  tuts

related: wx. 3 xx. 3 xw. *b3 oo. &#zx
   = Wythoffian o3x3x4x (grit) with cell list:
        8  gircoes
        32 trips
        16 tuts
1(-2)3:ABC wxx 3 ooo 3 xwx *b3 ooq &#zx
  → CRF with cell list:
        8  coes
        24 squobcues (J28)
        16 tets
        64 trips

related: wx. 3 oo. 3 xw. *b3 oo. &#zx
   = Wythoffian x3o3x4x (tat) with cell list:
        16 tets
        8  tics
134:ABC wxx 3 xxx 3 xwx *b3 xxw &#zx
  = Wythoffian x3x4o3x (prico) with cell list:
        96 hips
        24 sircoes
        24 toes
        96 trips

related: .xx 3 .xx 3 .wx *b3 .xw &#zx
   = Wythoffian x3x3x4x (gidpith) with cell list:
        8  gircoes
        32 hips
        24 ops
        16 toes
1(-2)34:ABC wxx 3 ooo 3 xwx *b3 xxw &#zx
  = Wythoffian x3o4x3o (srico) with cell list:
        24 coes
        24 sircoes
        6  trips

related: wx. 3 oo. 3 xw. *b3 xx. &#zx
   = Wythoffian x3o3x4x (proh) with cell list:
        16 coes
        24 ops
        8  tics
        32 trips
2:A2B2C2 wxx 3 ooo 3 xwx *b3 xxw &#zx
  = Wythoffian x3o4x3o (srico) with cell list:
        24 coes
        24 sircoes
        6  trips

related: wx. 3 oo. 3 xw. *b3 xx. &#zx
   = Wythoffian x3o3x4x (proh) with cell list:
        16 coes
        24 ops
        8  tics
        32 trips
(-1)2:A2B2C2 qoo 3 ooo 3 xwx *b3 xxw &#zx
  → CRF with cell list:
        8  coes
        24 squobcues (J28)
        16 tets
        64 trips

related: .oo 3 .oo 3 .wx *b3 .xw &#zx
   = Wythoffian x3o3x4x (tat) with cell list:
        16 tets
        8  tics
(-1)2(-3):A2B2C2 qoo 3 ooo 3 oqo *b3 xxw &#zx
  → CRF with cell list:
        24 esquidpies (J15)
        16 tets
        32 trips

related: qo. 3 oo. 3 oq. *b3 xx. &#zx
   = Wythoffian x3o3o4x (sidpith) with cell list:
        32 cubes
        16 tets
        32 trips
(-1)2(-3)(-4):A2B2C2 qoo 3 ooo 3 oqo *b3 ooq &#zx
  = Wythoffian x3o4o3o (ico) with cell list:
        24 octs

related: .oo 3 .oo 3 .qo *b3 .oq &#zx
  = Wythoffian o3o3o4x (tes) with cell list:
        8 cubes
 
using here node marks / (pseudo) edge lengths: Q=w+x=q+u, W=Q+x=w+u


EKF of the snub (dis)icositetrachoron (s3s4o3o)

©

in o3o3o *b3o subsymmetry   (up)
Representation:
fox 3 ooo 3 xfo *b3 oxf &#zx  (sadi)

with layer cycle:  A(1234) → B(3241) → C(4213) → A(1234)
All layers &
kaleido-facetings per layer:
A: f3o3x *b3o  →  A3: f3x3(-x) *b3o  →  A32: F3(-x)3o *b3x  →  A324: F3o3o *b3(-x)
B: o3o3f *b3x  →  B4: o3x3f *b3(-x)  →  B42: x3(-x)3F *b3o  →  B421: (-x)3o3F *b3o
C: x3o3o *b3f  →  C1: (-x)3x3o *b3f  →  C12: o3(-x)3x *b3F  →  C123: o3o3(-x) *b3F
A priori invalid combinations:
A    + C123
A3   + B42,C12
A32  + B4,C1
A324 + B
B4   + C12
B42  + C1
B421 + C   (all giving rise to u edges)
Other layer-combinations:
ABC1         fo(-x)3oox3xfo *b3oxf&#zx
ABC12        foo3oo(-x)3xfx *b3oxF&#zx → ‡ (f in A)
AB4C1        fo(-x)3oxx3xfo *b3o(-x)f&#zx → †
AB42C12      fxo3o(-x)(-x)3xFx *b3ooF&#zx → †
AB421C1      f(-x)(-x)3oox3xFo *b3oof&#zx → †
AB421C12     f(-x)o3oo(-x)3xFx *b3ooF&#zx → †
A3B4C1       fo(-x)3xxx3(-x)fo *b3o(-x)f&#zx → †
A3B4C123     foo3xxo3(-x)f(-x) *b3o(-x)F&#zx → †
A3B421C123   f(-x)o3xoo3(-x)F(-x) *b3ooF&#zx → †
A32B42C12    Fxo3(-x)(-x)(-x)3oFx *b3xoF&#zx → †
A32B42C123   Fxo3(-x)(-x)o3oF(-x) *b3xoF&#zx → †
A32B421C123  F(-x)o3(-x)oo3oF(-x) *b3xoF&#zx → †
A324B421C123 F(-x)o3ooo3oF(-x) *b3(-x)oF&#zx → †
Stott expansion:
(derived CRFs)
1:ABC1: Fxo 3 oox 3 xfo *b3 oxf &#zx
  → CRF with cell list:
        24 bilbiroes (J91)
        8  coes
        40 octs
        32 teddies (J63)
        40 tets
using here node marks / (pseudo) edge lengths: F=f+x

in o2o2o2o subsymmetry   (up)
Representation:
ooo|xxx|fff|FFF 2 Fxf|oFf|xFo|fxo 2 xfF|Ffo|Fox|xof 2 fFx|foF|oxF|ofx &#zx  (sadi)

with layer cycles:  
(ABCDEFGHIJKL)(1234) → (KFHAJIELBGDC)(3124) → (ILDGBKCFJAHE)(2431) → (BCAEFDHIGKLJ)(1423) → (JEGCLHDKAIFB)(4132) → (GJEHCLADKBIF)(4321) → (ABCDEFGHIJKL)(4321)
All layers &
kaleido-facetings per layer:
A: o2F2x2f  →  A3: o2F2(-x)2f
B: o2x2f2F  →  B2: o2(-x)2f2F
C: o2f2F2x  →  C4: o2f2F2(-x)

D: x2o2F2f  →  D1: (-x)2o2F2f
E: x2F2f2o  →  E1: (-x)2F2f2o
F: x2f2o2F  →  F1: (-x)2f2o2F

G: f2x2F2o  →  G2: f2(-x)2F2o
H: f2F2o2x  →  H4: f2F2o2(-x)
I: f2o2x2F  →  I3: f2o2(-x)2F

J: F2f2x2o  →  J3: F2f2(-x)2o
K: F2x2o2f  →  K2: F2(-x)2o2f
L: F2o2f2x  →  L4: F2o2f2(-x)
A priori invalid combinations:
A  + I3,J3
A3 + I,J
B  + G2,K2
B2 + G,K
C  + H4,L4
C4 + H,L
D  + E1,F1
D1 + E,F
E  + F1
E1 + F
G  + K2
G2 + K
H  + L4
H4 + L
I  + J3
I3 + J

(all giving rise to u edges)
Other layer-combinations:
ABCD1E1F1GHIJKL          ooo(-x)(-x)(-x)fffFFF 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx
ABC4D1E1F1GH4IJKL4       ooo(-x)(-x)(-x)fffFFF 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fF(-x)foFo(-x)Fof(-x) &#zx → ‡ (extremal f-edge DG)
AB2C4D1E1F1G2H4IJK2L4    ooo(-x)(-x)(-x)fffFFF 2 F(-x)foFf(-x)Fof(-x)o 2 xfFFfoFoxxof 2 fF(-x)foFo(-x)Fof(-x) &#zx → †
A3B2C4D1E1F1G2H4I3J3K2L4 ooo(-x)(-x)(-x)fffFFF 2 F(-x)foFf(-x)Fof(-x)o 2 (-x)fFFfoFo(-x)(-x)of 2 fF(-x)foFo(-x)Fof(-x) &#zx → †
Stott expansion:
(derived CRFs)
1:ABCD1E1F1GHIJKL: xxxoooFFFAAA 2 FxfoFfxFofxo 2 xfFFfoFoxxof 2 fFxfoFoxFofx &#zx
  → CRF with cell list:
        6  bilbiroes (J91)
        2  ikes
        36 squippies (J1)
        40 teddies (J63)
        36 tets
        8  trips
 
using here node marks / (pseudo) edge lengths: F=f+x, A=f+u=f+2x


EKF of the rectified tesseract (o3o3x4o)

©

in o2o3o4o subsymmetry   (up)
Representation:
qo 2 oo 3 xo 4 oq &#zx  (rit)
All layers &
kaleido-facetings per layer:
A: q2o3x4o  →  A3: q2x3(-x)4q
B: o2o3o4q
A priori invalid combinations:
neither can A+A3 be applied on either side (providing extremal u-edges)
(which thus excludes any mere . o3o4o symmetry)

nor can A3 be applied without an additional applied partial q-contraction
in the last node (else providing extremal q-edges)

even when using A only, then node 1 and node 4 still has to correspond, 
in order not to produce non-regular hexagons (i.e. diagonally elongated 
squares) there
Stott expansion:
(derived potential CRFs)
2:AB qo 2 xx 3 xo 4 oq &#zx
  → CRF with cell list:
        6  coes
        12 cubes
        2  toes
        16 tricues (J3)
14:AB wx 2 oo 3 xo 4 xw &#zx
  = Wythoffian o3o3x4x (tat) with cell list:
        16 tets
        8  tics
124:AB wx 2 xx 3 xo 4 xw &#zx
  → CRF with cell list:
        2  gircoes
        12 ops
        6  tics
        16 tricues (J3)
        8  trips
3(-q4):A3B qo 2 xo 3 ox 4 oo &#zx
  = Wythoffian x3o4o3o (ico) with cell list:
        24 octs
13(-q4):A3B wx 2 xo 3 ox 4 oo &#zx
  → CRF with cell list:
        6  esquidpies (J15)
        18 octs
        8  trips
34(-q4):A3B qo 2 xo 3 ox 4 xx &#zx
  → CRF with cell list:
        16 octs
        2  sircoes
        6  squobcues (J28)
        24 trips
134(-q4):A3B wx 2 xo 3 ox 4 xx &#zx
  = Wythoffian o3x3o4x (srit) with cell list:
        16 octs
        8  sircoes
        32 trips
 

in . o3o3o subsymmetry   (up)
Representation:
ooxx 3 oxxo 3 xxoo &#xt  (rit)

with inversive top-down-symmetry
All layers &
kaleido-facetings per layer:
A: o3o3x  →  A3: o3x3(-x)  →  A32: x3(-x)3o  →  A321 (-x)3o3o
B: o3x3x  →  B2: x3(-x)3u  →  B21: (-x)3o3u
          ↳  B3: o3u3(-x)
C: x3x3o  →  C1: (-x)3u3o
          ↳  C2: u3(-x)3x  →  C23: u3o3(-x)
D: x3o3o  →  D1: (-x)3x3o  →  D12: o3(-x)3x  →  D123: o3o3(-x)
A priori invalid combinations:
A    + B3,C23,D123
A3   + B,B2,B21,C2,D12
A32  + B,B21,B3,C,C1,D1
A321 + B2,C,C2,C23,D
B    + C2,C23,D12,D123
B2   + C,C1,C23,D1,D123
B21  + C,C2,C23,D,D123
B3   + C2,D12
C    + D1,D12
C1   + D,D12
C2   + D1,D123
C23  + D1,D12,D123
Other layer-combinations:
ABC1D1        oo(-x)(-x) 3 oxux 3 xxoo &#xt
AB2C2D        oxux 3 o(-x)(-x)o 3 xuxo &#xt
AB2C2D12      oxuo 3 o(-x)(-x)(-x) 3 xuxx &#xt → †
AB21C1D1      o(-x)(-x)(-x) 3 ooux 3 xuoo &#xt → †
A3B3CD123     ooxo 3 xuxo 3 (-x)(-x)o(-x) &#xt → †
A3B3C1D1      oo(-x)(-x) 3 xuux 3 (-x)(-x)oo &#xt
A3B3C1D123    oo(-x)o 3 xuuo 3 (-x)(-x)o(-x) &#xt → †
A32B2C2D12    xxuo 3 (-x)(-x)(-x)(-x) 3 ouxx &#xt → †
A321B3C1D123  (-x)o(-x)o 3 ouuo 3 o(-x)o(-x) &#xt → †
Stott expansion:
(derived potential CRFs)
1:ABC1D1 xxoo 3 oxux 3 xxoo &#xt
  → CRF with cell list:
        1 co
        6 cubes
        1 oct
        6 squippies (J1)
        8 tricues (J3)
        8 tuts

related: .xoo 3 .xux 3 .xoo &#xt (octum)
  → CRF with cell list:
        1 oct
        6 squippies (J1)
        1 toe
        8 tuts
2:AB2C2D oxux 3 xoox 3 xuxo &#xt
  = Wythoffian x3x3o4o (thex) with cell list:
        8  octs
        16 tuts
1(-2)3:A3B3C1D1 xxoo 3 oxxo 3 ooxx &#xt
  = Wythoffian o3o3x4o (rit) with cell list:
        8  coes
        16 tets

related: .xo. 3 .xx. 3 .ox. &#x (tutcup)
  → CRF (segmentochoron) with cell list:
        6 tets
        8 tricues (J3)
        2 tuts
 



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