Acronym sidpith
Name small disprismatotesseractihexadecachoron,
runcinated tesseract,
small prismated tesseract
 
©  
Cross sections
 ©
Circumradius sqrt[(3+sqrt(2))/2] = 1.485633
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o4o o3o3o . o3o . o o . o4o . o3o4o
1x3o3o4x x3o3o .
tet first
x3o . x
trip first
x . o4x
cube first
. o3o4x
cube first
2 x3o3q . o3o . w o . x4x . x3o4x
3 x3q3o . x3q . x w . o4x . x3o4x
4 o3o3w . o3q . w q . x4x . o3o4x
opposite cube
5 w3o3o . w3o . x w . o4x  
6 o3q3x . o3w . x o . x4x
7 q3o3x . q3o . w x . o4x
opposite cube
8 o3o3x .
opposite tet
q3x . x  
9   o3o . w
10 o3x . x
opposite trip
Lace city
in approx. ASCII-art
 ©  
     x4o    x4o     
                    
x4o  x4x    x4x  x4o
                    
                    
                    
x4o  x4x    x4x  x4o
                    
     x4o    x4o     
      o3x     o3x      
                       
o3o                 o3o
      q3x     q3x      
                       
q3o                 q3o
      o3w     o3w      
      w3o     w3o      
o3q                 o3q
                       
      x3q     x3q      
o3o                 o3o
                       
      x3o     x3o      
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: cube op sirco socco sroh tet trip
sidpith 3200001632
stefacoth 240800160
dippit 240080032
iquipadah 1680001632
shafipto 80800032
steth 80080160
snappoth 000081632
& others)
Dihedral angles
  • at {3} between tet and trip:   150°
  • at {4} between (axial) cube and trip:   arccos(-sqrt[2/3]) = 144.735610°
  • at {4} between (axial) cube and (full symmetrical) cube:   135°
Confer
blends:
ondip   iquipadah  
segmentochora:
cubasirco   sircope   sodip   squicuf  
related CRFs:
quawros   pex hex   pacsid pith   poxic  
decompositions:
hex || sidpith  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

As abstract polytope sidpith is isomorphic to quidpith, thereby replacing tet by inverted tet resp. an antipodium vertex figure by a frustrum one.

Note that sidpith can be thought of as the external blend of 1 hex + 16 tepes + 32 triddips + 32 squippyps + 8 cubpies. This decomposition is described as the degenerate segmentoteron xx3oo3oo4ox&#x.


Incidence matrix according to Dynkin symbol

x3o3o4x

. . . . | 64 |  3  3 |  3  6  3 |  1  3  3 1
--------+----+-------+----------+-----------
x . . . |  2 | 96  * |  2  2  0 |  1  2  1 0
. . . x |  2 |  * 96 |  0  2  2 |  0  1  2 1
--------+----+-------+----------+-----------
x3o . . |  3 |  3  0 | 64  *  * |  1  1  0 0
x . . x |  4 |  2  2 |  * 96  * |  0  1  1 0
. . o4x |  4 |  0  4 |  *  * 48 |  0  0  1 1
--------+----+-------+----------+-----------
x3o3o .   4 |  6  0 |  4  0  0 | 16  *  * *
x3o . x   6 |  6  3 |  2  3  0 |  * 32  * *
x . o4x   8 |  4  8 |  0  4  2 |  *  * 24 *
. o3o4x   8 |  0 12 |  0  0  6 |  *  *  * 8

snubbed forms: β3o3o4x, x3o3o4s, β3o3o4β

x3o3/2o4/3x

. .   .   . | 64 |  3  3 |  3  6  3 |  1  3  3 1
------------+----+-------+----------+-----------
x .   .   . |  2 | 96  * |  2  2  0 |  1  2  1 0
. .   .   x |  2 |  * 96 |  0  2  2 |  0  1  2 1
------------+----+-------+----------+-----------
x3o   .   . |  3 |  3  0 | 64  *  * |  1  1  0 0
x .   .   x |  4 |  2  2 |  * 96  * |  0  1  1 0
. .   o4/3x |  4 |  0  4 |  *  * 48 |  0  0  1 1
------------+----+-------+----------+-----------
x3o3/2o   .   4 |  6  0 |  4  0  0 | 16  *  * *
x3o   .   x   6 |  6  3 |  2  3  0 |  * 32  * *
x .   o4/3x   8 |  4  8 |  0  4  2 |  *  * 24 *
. o3/2o4/3x   8 |  0 12 |  0  0  6 |  *  *  * 8

x3/2o3o4/3x

.   . .   . | 64 |  3  3 |  3  6  3 |  1  3  3 1
------------+----+-------+----------+-----------
x   . .   . |  2 | 96  * |  2  2  0 |  1  2  1 0
.   . .   x |  2 |  * 96 |  0  2  2 |  0  1  2 1
------------+----+-------+----------+-----------
x3/2o .   . |  3 |  3  0 | 64  *  * |  1  1  0 0
x   . .   x |  4 |  2  2 |  * 96  * |  0  1  1 0
.   . o4/3x |  4 |  0  4 |  *  * 48 |  0  0  1 1
------------+----+-------+----------+-----------
x3/2o3o   .   4 |  6  0 |  4  0  0 | 16  *  * *
x3/2o .   x   6 |  6  3 |  2  3  0 |  * 32  * *
x   . o4/3x   8 |  4  8 |  0  4  2 |  *  * 24 *
.   o3o4/3x   8 |  0 12 |  0  0  6 |  *  *  * 8

x3/2o3/2o4x

.   .   . . | 64 |  3  3 |  3  6  3 |  1  3  3 1
------------+----+-------+----------+-----------
x   .   . . |  2 | 96  * |  2  2  0 |  1  2  1 0
.   .   . x |  2 |  * 96 |  0  2  2 |  0  1  2 1
------------+----+-------+----------+-----------
x3/2o   . . |  3 |  3  0 | 64  *  * |  1  1  0 0
x   .   . x |  4 |  2  2 |  * 96  * |  0  1  1 0
.   .   o4x |  4 |  0  4 |  *  * 48 |  0  0  1 1
------------+----+-------+----------+-----------
x3/2o3/2o .   4 |  6  0 |  4  0  0 | 16  *  * *
x3/2o   . x   6 |  6  3 |  2  3  0 |  * 32  * *
x   .   o4x   8 |  4  8 |  0  4  2 |  *  * 24 *
.   o3/2o4x   8 |  0 12 |  0  0  6 |  *  *  * 8

oxxo3oooo4xxxx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1
(cube || pseudo sirco || pseudo sirco || cube)

o...3o...4o...    | 8  *  * * |  3  3  0  0  0  0  0  0  0 | 3  3  6 0  0 0  0  0 0  0 0  0  0 0 | 1 1  3 3 0  0 0 0  0 0 0
.o..3.o..4.o..    | * 24  * * |  0  1  2  2  1  0  0  0  0 | 0  2  2 1  2 1  2  2 0  0 0  0  0 0 | 0 1  2 1 1  2 1 0  0 0 0
..o.3..o.4..o.    | *  * 24 * |  0  0  0  0  1  2  2  1  0 | 0  0  0 0  0 0  2  2 1  2 1  2  2 0 | 0 0  0 0 1  2 1 1  2 1 0
...o3...o4...o    | *  *  * 8 |  0  0  0  0  0  0  0  3  3 | 0  0  0 0  0 0  0  0 0  0 0  3  6 3 | 0 0  0 0 0  0 0 1  3 3 1
------------------+-----------+----------------------------+-------------------------------------+-------------------------
.... .... x...    | 2  0  0 0 | 12  *  *  *  *  *  *  *  * | 2  0  2 0  0 0  0  0 0  0 0  0  0 0 | 1 0  1 2 0  0 0 0  0 0 0
oo..3oo..4oo..&#x | 1  1  0 0 |  * 24  *  *  *  *  *  *  * | 0  2  2 0  0 0  0  0 0  0 0  0  0 0 | 0 1  2 1 0  0 0 0  0 0 0
.x.. .... ....    | 0  2  0 0 |  *  * 24  *  *  *  *  *  * | 0  1  0 1  1 0  1  0 0  0 0  0  0 0 | 0 1  1 0 1  1 0 0  0 0 0
.... .... .x..    | 0  2  0 0 |  *  *  * 24  *  *  *  *  * | 0  0  1 0  1 1  0  1 0  0 0  0  0 0 | 0 0  1 1 0  1 1 0  0 0 0
.oo.3.oo.4.oo.&#x | 0  1  1 0 |  *  *  *  * 24  *  *  *  * | 0  0  0 0  0 0  2  2 0  0 0  0  0 0 | 0 0  0 0 1  2 1 0  0 0 0
..x. .... ....    | 0  0  2 0 |  *  *  *  *  * 24  *  *  * | 0  0  0 0  0 0  1  0 1  1 0  1  0 0 | 0 0  0 0 1  1 0 1  1 0 0
.... .... ..x.    | 0  0  2 0 |  *  *  *  *  *  * 24  *  * | 0  0  0 0  0 0  0  1 0  1 1  0  1 0 | 0 0  0 0 0  1 1 0  1 1 0
..oo3..oo4..oo&#x | 0  0  1 1 |  *  *  *  *  *  *  * 24  * | 0  0  0 0  0 0  0  0 0  0 0  2  2 0 | 0 0  0 0 0  0 0 1  2 1 0
.... .... ...x    | 0  0  0 2 |  *  *  *  *  *  *  *  * 12 | 0  0  0 0  0 0  0  0 0  0 0  0  2 2 | 0 0  0 0 0  0 0 0  1 2 1
------------------+-----------+----------------------------+-------------------------------------+-------------------------
.... o...4x...    | 4  0  0 0 |  4  0  0  0  0  0  0  0  0 | 6  *  * *  * *  *  * *  * *  *  * * | 1 0  0 1 0  0 0 0  0 0 0
ox.. .... ....&#x | 1  2  0 0 |  0  2  1  0  0  0  0  0  0 | * 24  * *  * *  *  * *  * *  *  * * | 0 1  1 0 0  0 0 0  0 0 0
.... .... xx..&#x | 2  2  0 0 |  1  2  0  1  0  0  0  0  0 | *  * 24 *  * *  *  * *  * *  *  * * | 0 0  1 1 0  0 0 0  0 0 0
.x..3.o.. ....    | 0  3  0 0 |  0  0  3  0  0  0  0  0  0 | *  *  * 8  * *  *  * *  * *  *  * * | 0 1  0 0 1  0 0 0  0 0 0
.x.. .... .x..    | 0  4  0 0 |  0  0  2  2  0  0  0  0  0 | *  *  * * 12 *  *  * *  * *  *  * * | 0 0  1 0 0  1 0 0  0 0 0
.... .o..4.x..    | 0  4  0 0 |  0  0  0  4  0  0  0  0  0 | *  *  * *  * 6  *  * *  * *  *  * * | 0 0  0 1 0  0 1 0  0 0 0
.xx. .... ....&#x | 0  2  2 0 |  0  0  1  0  2  1  0  0  0 | *  *  * *  * * 24  * *  * *  *  * * | 0 0  0 0 1  1 0 0  0 0 0
.... .... .xx.&#x | 0  2  2 0 |  0  0  0  1  2  0  1  0  0 | *  *  * *  * *  * 24 *  * *  *  * * | 0 0  0 0 0  1 1 0  0 0 0
..x.3..o. ....    | 0  0  3 0 |  0  0  0  0  0  3  0  0  0 | *  *  * *  * *  *  * 8  * *  *  * * | 0 0  0 0 1  0 0 1  0 0 0
..x. .... ..x.    | 0  0  4 0 |  0  0  0  0  0  2  2  0  0 | *  *  * *  * *  *  * * 12 *  *  * * | 0 0  0 0 0  1 0 0  1 0 0
.... ..o.4..x.    | 0  0  4 0 |  0  0  0  0  0  0  4  0  0 | *  *  * *  * *  *  * *  * 6  *  * * | 0 0  0 0 0  0 1 0  0 1 0
..xo .... ....&#x | 0  0  2 1 |  0  0  0  0  0  1  0  2  0 | *  *  * *  * *  *  * *  * * 24  * * | 0 0  0 0 0  0 0 1  1 0 0
.... .... ..xx&#x | 0  0  2 2 |  0  0  0  0  0  0  1  2  1 | *  *  * *  * *  *  * *  * *  * 24 * | 0 0  0 0 0  0 0 0  1 1 0
.... ...o4...x    | 0  0  0 4 |  0  0  0  0  0  0  0  0  4 | *  *  * *  * *  *  * *  * *  *  * 6 | 0 0  0 0 0  0 0 0  0 1 1
------------------+-----------+----------------------------+-------------------------------------+-------------------------
o...3o...4x...     8  0  0 0 | 12  0  0  0  0  0  0  0  0 | 6  0  0 0  0 0  0  0 0  0 0  0  0 0 | 1 *  * * *  * * *  * * *
ox..3oo.. ....&#x  1  3  0 0 |  0  3  3  0  0  0  0  0  0 | 0  3  0 1  0 0  0  0 0  0 0  0  0 0 | * 8  * * *  * * *  * * *
ox.. .... xx..&#x  2  4  0 0 |  1  4  2  2  0  0  0  0  0 | 0  2  2 0  1 0  0  0 0  0 0  0  0 0 | * * 12 * *  * * *  * * *
.... oo..4xx..&#x  4  4  0 0 |  4  4  0  4  0  0  0  0  0 | 1  0  4 0  0 1  0  0 0  0 0  0  0 0 | * *  * 6 *  * * *  * * *
.xx.3.oo. ....&#x  0  3  3 0 |  0  0  3  0  3  3  0  0  0 | 0  0  0 1  0 0  3  0 1  0 0  0  0 0 | * *  * * 8  * * *  * * *
.xx. .... .xx.&#x  0  4  4 0 |  0  0  2  2  4  2  2  0  0 | 0  0  0 0  1 0  2  2 0  1 0  0  0 0 | * *  * * * 12 * *  * * *
.... .oo.4.xx.&#x  0  4  4 0 |  0  0  0  4  4  0  4  0  0 | 0  0  0 0  0 1  0  4 0  0 1  0  0 0 | * *  * * *  * 6 *  * * *
..xo3..oo ....&#x  0  0  3 1 |  0  0  0  0  0  3  0  3  0 | 0  0  0 0  0 0  0  0 1  0 0  3  0 0 | * *  * * *  * * 8  * * *
..xo .... ..xx&#x  0  0  4 2 |  0  0  0  0  0  2  2  4  1 | 0  0  0 0  0 0  0  0 0  1 0  2  2 0 | * *  * * *  * * * 12 * *
.... ..oo4..xx&#x  0  0  4 4 |  0  0  0  0  0  0  4  4  4 | 0  0  0 0  0 0  0  0 0  0 1  0  4 1 | * *  * * *  * * *  * 6 *
...o3...o4...x     0  0  0 8 |  0  0  0  0  0  0  0  0 12 | 0  0  0 0  0 0  0  0 0  0 0  0  0 6 | * *  * * *  * * *  * * 1
or
o...3o...4o...    & | 16  * |  3  3  0  0  0 |  3  3  6  0  0  0  0  0 | 1  1  3  3 0  0 0
.o..3.o..4.o..    & |  * 48 |  0  1  2  2  1 |  0  2  2  1  2  1  2  2 | 0  1  2  1 1  2 1
--------------------+-------+----------------+-------------------------+------------------
.... .... x...    & |  2  0 | 24  *  *  *  * |  2  0  2  0  0  0  0  0 | 1  0  1  2 0  0 0
oo..3oo..4oo..&#x & |  1  1 |  * 48  *  *  * |  0  2  2  0  0  0  0  0 | 0  1  2  1 0  0 0
.x.. .... ....    & |  0  2 |  *  * 48  *  * |  0  1  0  1  1  0  1  0 | 0  1  1  0 1  1 0
.... .... .x..    & |  0  2 |  *  *  * 48  * |  0  0  1  0  1  1  0  1 | 0  0  1  1 0  1 1
.oo.3.oo.4.oo.&#x   |  0  2 |  *  *  *  * 24 |  0  0  0  0  0  0  2  2 | 0  0  0  0 1  2 1
--------------------+-------+----------------+-------------------------+------------------
.... o...4x...    & |  4  0 |  4  0  0  0  0 | 12  *  *  *  *  *  *  * | 1  0  0  1 0  0 0
ox.. .... ....&#x & |  1  2 |  0  2  1  0  0 |  * 48  *  *  *  *  *  * | 0  1  1  0 0  0 0
.... .... xx..&#x & |  2  2 |  1  2  0  1  0 |  *  * 48  *  *  *  *  * | 0  0  1  1 0  0 0
.x..3.o.. ....    & |  0  3 |  0  0  3  0  0 |  *  *  * 16  *  *  *  * | 0  1  0  0 1  0 0
.x.. .... .x..    & |  0  4 |  0  0  2  2  0 |  *  *  *  * 24  *  *  * | 0  0  1  0 0  1 0
.... .o..4.x..    & |  0  4 |  0  0  0  4  0 |  *  *  *  *  * 12  *  * | 0  0  0  1 0  0 1
.xx. .... ....&#x   |  0  4 |  0  0  2  0  2 |  *  *  *  *  *  * 24  * | 0  0  0  0 1  1 0
.... .... .xx.&#x   |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  *  * 24 | 0  0  0  0 0  1 1
--------------------+-------+----------------+-------------------------+------------------
o...3o...4x...    &   8  0 | 12  0  0  0  0 |  6  0  0  0  0  0  0  0 | 2  *  *  * *  * *
ox..3oo.. ....&#x &   1  3 |  0  3  3  0  0 |  0  3  0  1  0  0  0  0 | * 16  *  * *  * *
ox.. .... xx..&#x &   2  4 |  1  4  2  2  0 |  0  2  2  0  1  0  0  0 | *  * 24  * *  * *
.... oo..4xx..&#x &   4  4 |  4  4  0  4  0 |  1  0  4  0  0  1  0  0 | *  *  * 12 *  * *
.xx.3.oo. ....&#x     0  6 |  0  0  6  0  3 |  0  0  0  2  0  0  3  0 | *  *  *  * 8  * *
.xx. .... .xx.&#x     0  8 |  0  0  4  4  4 |  0  0  0  0  2  0  2  2 | *  *  *  * * 12 *
.... .oo.4.xx.&#x     0  8 |  0  0  0  8  4 |  0  0  0  0  0  2  0  4 | *  *  *  * *  * 6

xxxowoqo3ooqooqoo3oqowoxxx&#xt   → height(1,2) = height(2,3) = height(6,7) = height(7,8) = 1/2
                                      height(3,4) = height(5,6) = (sqrt(2)-1)/2 = 0.207107
                                      height(4,5) = (2-sqrt(2))/2 = 0.292893
(tet || pseudo (x,q)-co || pseudo (x,q)-tut || pseudo inv w-tet || pseudo w-tet || pseudo inv (x,q)-tut || pseudo (q,x)-co || dual tet)

o.......3o.......3o.......      & | 8  *  * * |  3  3  0  0  0  0  0  0 | 3  6  3 0  0  0  0  0  0 | 1 3  3 1 0  0  0 0
.o......3.o......3.o......      & | * 24  * * |  0  1  2  2  1  0  0  0 | 0  2  2 1  2  2  1  2  0 | 0 1  2 1 1  2  1 0
..o.....3..o.....3..o.....      & | *  * 24 * |  0  0  0  2  0  1  1  2 | 0  0  1 0  2  0  2  4  3 | 0 0  1 1 0  3  2 1
...o....3...o....3...o....      & | *  *  * 8 |  0  0  0  0  3  0  3  0 | 0  0  0 0  0  3  3  6  0 | 0 0  0 1 1  3  3 0
----------------------------------+-----------+-------------------------+--------------------------+-------------------
x....... ........ ........      & | 2  0  0 0 | 12  *  *  *  *  *  *  * | 2  2  0 0  0  0  0  0  0 | 1 2  1 0 0  0  0 0
oo......3oo......3oo......&#x   & | 1  1  0 0 |  * 24  *  *  *  *  *  * | 0  2  2 0  0  0  0  0  0 | 0 1  2 1 0  0  0 0
.x...... ........ ........      & | 0  2  0 0 |  *  * 24  *  *  *  *  * | 0  1  0 1  1  1  0  0  0 | 0 1  1 0 1  1  0 0
.oo.....3.oo.....3.oo.....&#x   & | 0  1  1 0 |  *  *  * 48  *  *  *  * | 0  0  1 0  1  0  1  1  0 | 0 0  1 1 0  1  1 0
.o.o....3.o.o....3.o.o....&#x   & | 0  1  0 1 |  *  *  *  * 24  *  *  * | 0  0  0 0  0  2  0  2  0 | 0 0  0 0 1  2  1 0
..x..... ........ ........      & | 0  0  2 0 |  *  *  *  *  * 12  *  * | 0  0  0 0  2  0  0  0  2 | 0 0  1 0 0  2  0 1
..o.o...3..o.o...3..o.o...&#x   & | 0  0  1 1 |  *  *  *  *  *  * 24  * | 0  0  0 0  0  0  2  2  0 | 0 0  0 1 0  1  2 0
..o..o..3..o..o..3..o..o..&#x     | 0  0  2 0 |  *  *  *  *  *  *  * 24 | 0  0  0 0  0  0  0  2  2 | 0 0  0 0 0  2  1 1
----------------------------------+-----------+-------------------------+--------------------------+-------------------
x.......3o....... ........      & | 3  0  0 0 |  3  0  0  0  0  0  0  0 | 8  *  * *  *  *  *  *  * | 1 1  0 0 0  0  0 0
xx...... ........ ........&#x   & | 2  2  0 0 |  1  2  1  0  0  0  0  0 | * 24  * *  *  *  *  *  * | 0 1  1 0 0  0  0 0
........ ........ oqo.....&#xt  & | 1  2  1 0 |  0  2  0  2  0  0  0  0 | *  * 24 *  *  *  *  *  * | 0 0  1 1 0  0  0 0
.x......3.o...... ........      & | 0  3  0 0 |  0  0  3  0  0  0  0  0 | *  *  * 8  *  *  *  *  * | 0 1  0 0 1  0  0 0
.xx..... ........ ........&#x   & | 0  2  2 0 |  0  0  1  2  0  1  0  0 | *  *  * * 24  *  *  *  * | 0 0  1 0 0  1  0 0
.x.o.... ........ ........&#x   & | 0  2  0 1 |  0  0  1  0  2  0  0  0 | *  *  * *  * 24  *  *  * | 0 0  0 0 1  1  0 0
........ .oq.o... ........&#xt  & | 0  1  2 1 |  0  0  0  2  0  0  2  0 | *  *  * *  *  * 24  *  * | 0 0  0 1 0  0  1 0
.ooo.o..3.ooo.o..3.ooo.o..&#xt  & | 0  1  2 1 |  0  0  0  1  1  0  1  1 | *  *  * *  *  *  * 48  * | 0 0  0 0 0  1  1 0
..x..o.. ........ ........&#x   & | 0  0  3 0 |  0  0  0  0  0  1  0  2 | *  *  * *  *  *  *  * 24 | 0 0  0 0 0  1  0 1
----------------------------------+-----------+-------------------------+--------------------------+-------------------
x.......3o.......3o.......      &  4  0  0 0 |  6  0  0  0  0  0  0  0 | 4  0  0 0  0  0  0  0  0 | 2 *  * * *  *  * *
xx......3oo...... ........&#x   &  3  3  0 0 |  3  3  3  0  0  0  0  0 | 1  3  0 1  0  0  0  0  0 | * 8  * * *  *  * *
xxx..... ........ oqo.....&#xt  &  2  4  2 0 |  1  4  2  4  0  1  0  0 | 0  2  2 0  2  0  0  0  0 | * * 12 * *  *  * *
........ ooq.o...3oqo.o...&#xt  &  1  3  3 1 |  0  3  0  6  0  0  3  0 | 0  0  3 0  0  0  3  0  0 | * *  * 8 *  *  * *
.x.o....3.o.o.... ........&#x   &  0  3  0 1 |  0  0  3  0  3  0  0  0 | 0  0  0 1  0  3  0  0  0 | * *  * * 8  *  * *
.xxo.o.. ........ ........&#xt  &  0  2  3 1 |  0  0  1  2  2  1  1  2 | 0  0  0 0  1  1  0  2  1 | * *  * * * 24  * *
........ .oqooqo. ........&#xt     0  2  4 2 |  0  0  0  4  2  0  4  2 | 0  0  0 0  0  0  2  4  0 | * *  * * *  * 12 *
..x..o.. ........ ..o..x..&#x      0  0  4 0 |  0  0  0  0  0  2  0  4 | 0  0  0 0  0  0  0  0  4 | * *  * * *  *  * 6

xowqwox xxxxxxx4oxoxoxox&#xt   → height(1,2) = height(3,4) = height(4,5) = height(6,7) = 1/2
                                 height(2,3) = height(5,6) = (sqrt(2)-1)/2 = 0.207107
(cube || pseudo {8} || pseudo (w,x,x)-cube || pseudo (q,x)-op || pseudo (w,x,x)-cube || pseudo {8} || cube)

o...... o......4o......      & | 16  *  *  * | 1  2  2  1 0 0  0  0  0 0 0 0 | 2 1  2  2  1  2  2 0  0  0 0  0  0 0  0 | 1 2 1 1  2  1 0 0 0 0 0
.o..... .o.....4.o.....      & |  * 16  *  * | 0  0  2  0 1 1  2  0  0 0 0 0 | 0 0  1  2  2  0  2 1  2  2 0  0  0 0  0 | 0 1 1 0  2  2 1 1 0 0 0
..o.... ..o....4..o....      & |  *  * 16  * | 0  0  0  1 0 0  0  2  2 1 0 0 | 0 0  0  0  0  2  2 0  0  0 1  2  1 2  2 | 0 0 0 1  2  1 0 0 2 2 1
...o... ...o...4...o...        |  *  *  * 16 | 0  0  0  0 0 0  2  0  2 0 1 1 | 0 0  0  0  0  0  2 1  2  2 0  2  2 0  1 | 0 0 0 0  2  2 1 1 0 1 1
-------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------
x...... ....... .......      & |  2  0  0  0 | 8  *  *  * * *  *  *  * * * * | 2 0  2  0  0  0  0 0  0  0 0  0  0 0  0 | 1 2 1 0  0  0 0 0 0 0 0
....... x...... .......      & |  2  0  0  0 | * 16  *  * * *  *  *  * * * * | 1 1  0  1  0  1  0 0  0  0 0  0  0 0  0 | 1 1 0 1  1  0 0 0 0 0 0
oo..... oo.....4oo.....&#x   & |  1  1  0  0 | *  * 32  * * *  *  *  * * * * | 0 0  1  1  1  0  1 0  0  0 0  0  0 0  0 | 0 1 1 0  1  1 0 0 0 0 0
o.o.... o.o....4o.o....&#x   & |  1  0  1  0 | *  *  * 16 * *  *  *  * * * * | 0 0  0  0  0  2  2 0  0  0 0  0  0 0  0 | 0 0 0 1  2  1 0 0 0 0 0
....... .x..... .......      & |  0  2  0  0 | *  *  *  * 8 *  *  *  * * * * | 0 0  0  2  0  0  0 0  2  0 0  0  0 0  0 | 0 1 0 0  2  0 1 0 0 0 0
....... ....... .x.....      & |  0  2  0  0 | *  *  *  * * 8  *  *  * * * * | 0 0  0  0  2  0  0 0  0  2 0  0  0 0  0 | 0 0 1 0  0  2 0 1 0 0 0
.o.o... .o.o...4.o.o...&#x   & |  0  1  0  1 | *  *  *  * * * 32  *  * * * * | 0 0  0  0  0  0  1 1  1  1 0  0  0 0  0 | 0 0 0 0  1  1 1 1 0 0 0
....... ..x.... .......      & |  0  0  2  0 | *  *  *  * * *  * 16  * * * * | 0 0  0  0  0  1  0 0  0  0 1  1  0 1  0 | 0 0 0 1  1  0 0 0 1 1 0
..oo... ..oo...4..oo...&#x   & |  0  0  1  1 | *  *  *  * * *  *  * 32 * * * | 0 0  0  0  0  0  1 0  0  0 0  1  1 0  1 | 0 0 0 0  1  1 0 0 0 1 1
..o.o.. ..o.o..4..o.o..&#x     |  0  0  2  0 | *  *  *  * * *  *  *  * 8 * * | 0 0  0  0  0  0  0 0  0  0 0  0  0 2  2 | 0 0 0 0  0  0 0 0 1 2 1
....... ...x... .......        |  0  0  0  2 | *  *  *  * * *  *  *  * * 8 * | 0 0  0  0  0  0  0 0  2  0 0  2  0 0  0 | 0 0 0 0  2  0 1 0 0 1 0
....... ....... ...x...        |  0  0  0  2 | *  *  *  * * *  *  *  * * * 8 | 0 0  0  0  0  0  0 0  0  2 0  0  2 0  0 | 0 0 0 0  0  2 0 1 0 0 1
-------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------
x...... x...... .......      & |  4  0  0  0 | 2  2  0  0 0 0  0  0  0 0 0 0 | 8 *  *  *  *  *  * *  *  * *  *  * *  * | 1 1 0 0  0  0 0 0 0 0 0
....... x......4o......      & |  4  0  0  0 | 0  4  0  0 0 0  0  0  0 0 0 0 | * 4  *  *  *  *  * *  *  * *  *  * *  * | 1 0 0 1  0  0 0 0 0 0 0
xo..... ....... .......&#x   & |  2  1  0  0 | 1  0  2  0 0 0  0  0  0 0 0 0 | * * 16  *  *  *  * *  *  * *  *  * *  * | 0 1 1 0  0  0 0 0 0 0 0
....... xx..... .......&#x   & |  2  2  0  0 | 0  1  2  0 1 0  0  0  0 0 0 0 | * *  * 16  *  *  * *  *  * *  *  * *  * | 0 1 0 0  1  0 0 0 0 0 0
....... ....... ox.....&#x   & |  1  2  0  0 | 0  0  2  0 0 1  0  0  0 0 0 0 | * *  *  * 16  *  * *  *  * *  *  * *  * | 0 0 1 0  0  1 0 0 0 0 0
....... x.x.... .......&#x   & |  2  0  2  0 | 0  1  0  2 0 0  0  1  0 0 0 0 | * *  *  *  * 16  * *  *  * *  *  * *  * | 0 0 0 1  1  0 0 0 0 0 0
oooo... oooo...4oooo...&#xr  & |  1  1  1  1 | 0  0  1  1 0 0  1  0  1 0 0 0 | * *  *  *  *  * 32 *  *  * *  *  * *  * | 0 0 0 0  1  1 0 0 0 0 0
.o.q.o. ....... .......&#xt    |  0  2  0  2 | 0  0  0  0 0 0  4  0  0 0 0 0 | * *  *  *  *  *  * 8  *  * *  *  * *  * | 0 0 0 0  0  0 1 1 0 0 0
....... .x.x... .......&#x   & |  0  2  0  2 | 0  0  0  0 1 0  2  0  0 0 1 0 | * *  *  *  *  *  * * 16  * *  *  * *  * | 0 0 0 0  1  0 1 0 0 0 0
....... ....... .x.x...&#x   & |  0  2  0  2 | 0  0  0  0 0 1  2  0  0 0 0 1 | * *  *  *  *  *  * *  * 16 *  *  * *  * | 0 0 0 0  0  1 0 1 0 0 0
....... ..x....4..o....      & |  0  0  4  0 | 0  0  0  0 0 0  0  4  0 0 0 0 | * *  *  *  *  *  * *  *  * 4  *  * *  * | 0 0 0 1  0  0 0 0 1 0 0
....... ..xx... .......&#x   & |  0  0  2  2 | 0  0  0  0 0 0  0  1  2 0 1 0 | * *  *  *  *  *  * *  *  * * 16  * *  * | 0 0 0 0  1  0 0 0 0 1 0
....... ....... ..ox...&#x   & |  0  0  1  2 | 0  0  0  0 0 0  0  0  2 0 0 1 | * *  *  *  *  *  * *  *  * *  * 16 *  * | 0 0 0 0  0  1 0 0 0 0 1
....... ..x.x.. .......&#x     |  0  0  4  0 | 0  0  0  0 0 0  0  2  0 2 0 0 | * *  *  *  *  *  * *  *  * *  *  * 8  * | 0 0 0 0  0  0 0 0 1 1 0
..ooo.. ..ooo..4..ooo..&#x     |  0  0  2  1 | 0  0  0  0 0 0  0  0  2 1 0 0 | * *  *  *  *  *  * *  *  * *  *  * * 16 | 0 0 0 0  0  0 0 0 0 1 1
-------------------------------+-------------+-------------------------------+-----------------------------------------+------------------------
x...... x......4o......      &   8  0  0  0 | 4  8  0  0 0 0  0  0  0 0 0 0 | 4 2  0  0  0  0  0 0  0  0 0  0  0 0  0 | 2 * * *  *  * * * * * *
xo..... xx..... .......&#x   &   4  2  0  0 | 2  2  4  0 1 0  0  0  0 0 0 0 | 1 0  2  2  0  0  0 0  0  0 0  0  0 0  0 | * 8 * *  *  * * * * * *
xo..... ....... ox.....&#x   &   2  2  0  0 | 1  0  4  0 0 1  0  0  0 0 0 0 | 0 0  2  0  2  0  0 0  0  0 0  0  0 0  0 | * * 8 *  *  * * * * * *
....... x.x....4o.o....&#x   &   4  0  4  0 | 0  4  0  4 0 0  0  4  0 0 0 0 | 0 1  0  0  0  4  0 0  0  0 1  0  0 0  0 | * * * 4  *  * * * * * *
....... xxxx... .......&#xr  &   2  2  2  2 | 0  1  2  2 1 0  2  1  2 0 1 0 | 0 0  0  1  0  1  2 0  1  0 0  1  0 0  0 | * * * * 16  * * * * * *
....... ....... oxox...&#xr  &   1  2  1  2 | 0  0  2  1 0 1  2  0  2 0 0 1 | 0 0  0  0  1  0  2 0  0  1 0  0  1 0  0 | * * * *  * 16 * * * * *
.o.q.o. .x.x.x. .......&#xt      0  4  0  4 | 0  0  0  0 2 0  8  0  0 0 2 0 | 0 0  0  0  0  0  0 2  4  0 0  0  0 0  0 | * * * *  *  * 4 * * * *
.o.q.o. ....... .x.x.x.&#xt      0  4  0  4 | 0  0  0  0 0 2  8  0  0 0 0 2 | 0 0  0  0  0  0  0 2  0  4 0  0  0 0  0 | * * * *  *  * * 4 * * *
....... ..x.x..4..o.o..&#x       0  0  8  0 | 0  0  0  0 0 0  0  8  0 4 0 0 | 0 0  0  0  0  0  0 0  0  0 2  0  0 4  0 | * * * *  *  * * * 2 * *
....... ..xxx.. .......&#x       0  0  4  2 | 0  0  0  0 0 0  0  2  4 2 1 0 | 0 0  0  0  0  0  0 0  0  0 0  2  0 1  2 | * * * *  *  * * * * 8 *
....... ....... ..oxo..&#x       0  0  2  2 | 0  0  0  0 0 0  0  0  4 1 0 1 | 0 0  0  0  0  0  0 0  0  0 0  0  2 0  2 | * * * *  *  * * * * * 8

qo3oo3oq *b3xx&#zx   → height = 0
(tegum sum of 2 mutually gyrated (x,q)-rits)

o.3o.3o. *b3o.     | 32  * |  3  3  0 |  3  3  6  0 | 1 1  3  3 0
.o3.o3.o *b3.o     |  * 32 |  0  3  3 |  0  3  6  3 | 0 1  3  3 1
-------------------+-------+----------+-------------+------------
.. .. ..    x.     |  2  0 | 48  *  * |  2  0  2  0 | 1 0  1  2 0
oo3oo3oo *b3oo&#x  |  1  1 |  * 96  * |  0  2  2  0 | 0 1  2  1 0
.. .. ..    .x     |  0  2 |  *  * 48 |  0  0  2  2 | 0 0  1  2 1
-------------------+-------+----------+-------------+------------
.. o. .. *b3x.     |  3  0 |  3  0  0 | 32  *  *  * | 1 0  0  1 0
qo .. oq    ..&#zx |  2  2 |  0  4  0 |  * 48  *  * | 0 1  1  0 0
.. .. ..    xx&#x  |  2  2 |  1  2  1 |  *  * 96  * | 0 0  1  1 0
.. .o .. *b3.x     |  0  3 |  0  0  3 |  *  *  * 32 | 0 0  0  1 1
-------------------+-------+----------+-------------+------------
.. o.3o. *b3x.       4  0 |  6  0  0 |  4  0  0  0 | 8 *  *  * *
qo3oo3oq    ..&#zx   4  4 |  0 12  0 |  0  6  0  0 | * 8  *  * *
qo .. oq    xx&#zx   4  4 |  2  8  2 |  0  2  4  0 | * * 24  * *
.. oo .. *b3xx&#x    3  3 |  3  3  3 |  1  0  3  1 | * *  * 32 *
.o3.o .. *b3.x       0  4 |  0  0  6 |  0  0  0  4 | * *  *  * 8

wx ox3oo4xx&#zx   → height = 0
(tegum sum of (w,x,x,x)-tes and sircope)

o. o.3o.4o.     | 16  * |  3  3  0  0  0 |  3  3  6  0  0  0  0  0 | 1  1  3  3 0  0 0
.o .o3.o4.o     |  * 48 |  0  1  1  2  2 |  0  2  2  2  2  1  2  1 | 0  1  2  1 1  2 1
----------------+-------+----------------+-------------------------+------------------
.. .. .. x.     |  2  0 | 24  *  *  *  * |  2  0  2  0  0  0  0  0 | 1  0  1  2 0  0 0
oo oo3oo4oo&#x  |  1  1 |  * 48  *  *  * |  0  2  2  0  0  0  0  0 | 0  1  2  1 0  0 0
.x .. .. ..     |  0  2 |  *  * 24  *  * |  0  0  0  2  2  0  0  0 | 0  0  0  0 1  2 1
.. .x .. ..     |  0  2 |  *  *  * 48  * |  0  1  0  1  0  1  1  0 | 0  1  1  0 1  1 0
.. .. .. .x     |  0  2 |  *  *  *  * 48 |  0  0  1  0  1  0  1  1 | 0  0  1  1 0  1 1
----------------+-------+----------------+-------------------------+------------------
.. .. o.4x.     |  4  0 |  4  0  0  0  0 | 12  *  *  *  *  *  *  * | 1  0  0  1 0  0 0
.. ox .. ..&#x  |  1  2 |  0  2  0  1  0 |  * 48  *  *  *  *  *  * | 0  1  1  0 0  0 0
.. .. .. xx&#x  |  2  2 |  1  2  0  0  1 |  *  * 48  *  *  *  *  * | 0  0  1  1 0  0 0
.x .x .. ..     |  0  4 |  0  0  2  2  0 |  *  *  * 24  *  *  *  * | 0  0  0  0 1  1 0
.x .. .. .x     |  0  4 |  0  0  2  0  2 |  *  *  *  * 24  *  *  * | 0  0  0  0 0  1 1
.. .x3.o ..     |  0  3 |  0  0  0  3  0 |  *  *  *  *  * 16  *  * | 0  1  0  0 1  0 0
.. .x .. .x     |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  * 24  * | 0  0  1  0 0  1 0
.. .. .o4.x     |  0  4 |  0  0  0  0  4 |  *  *  *  *  *  *  * 12 | 0  0  0  1 0  0 1
----------------+-------+----------------+-------------------------+------------------
.. o.3o.4x.       8  0 | 12  0  0  0  0 |  6  0  0  0  0  0  0  0 | 2  *  *  * *  * *
.. ox3oo ..&#x    1  3 |  0  3  0  3  0 |  0  3  0  0  0  1  0  0 | * 16  *  * *  * *
.. ox .. xx&#x    2  4 |  1  4  0  2  2 |  0  2  2  0  0  0  1  0 | *  * 24  * *  * *
.. .. oo4xx&#x    4  4 |  4  4  0  0  4 |  1  0  4  0  0  0  0  1 | *  *  * 12 *  * *
.x .x3.o ..       0  6 |  0  0  3  6  0 |  0  0  0  3  0  2  0  0 | *  *  *  * 8  * *
.x .x .. .x       0  8 |  0  0  4  4  4 |  0  0  0  2  2  0  2  0 | *  *  *  * * 12 *
.x .. .o4.x       0  8 |  0  0  4  0  8 |  0  0  0  0  4  0  0  2 | *  *  *  * *  * 6

xo4xx ox4xx&#zx   → height = 0
(tegum sum of 2 interchanged sodips.)

o.4o. o.4o.     & | 64 |  1  1  2  2 |  2  2  1  3  4 | 1 1  1  3  2
------------------+----+-------------+----------------+-------------
x. .. .. ..     & |  2 | 32  *  *  * |  2  0  0  2  0 | 1 0  1  2  0
.. x. .. ..     & |  2 |  * 32  *  * |  0  2  0  0  2 | 0 1  0  1  2
.. .. .. x.     & |  2 |  *  * 64  * |  1  1  1  0  1 | 1 1  0  1  1
oo4oo oo4oo&#x    |  2 |  *  *  * 64 |  0  0  0  2  2 | 0 0  1  2  1
------------------+----+-------------+----------------+-------------
x. .. .. x.     & |  4 |  2  0  2  0 | 32  *  *  *  * | 1 0  0  1  0
.. x. .. x.     & |  4 |  0  2  2  0 |  * 32  *  *  * | 0 1  0  0  1
.. .. o.4x.     & |  4 |  0  0  4  0 |  *  * 16  *  * | 1 1  0  0  0
xo .. .. ..&#x  & |  3 |  1  0  0  2 |  *  *  * 64  * | 0 0  1  1  0
.. xx .. ..&#x  & |  4 |  0  1  1  2 |  *  *  *  * 64 | 0 0  0  1  1
------------------+----+-------------+----------------+-------------
x. .. o.4x.     &   8 |  4  0  8  0 |  4  0  2  0  0 | 8 *  *  *  *
.. x. o.4x.     &   8 |  0  4  8  0 |  0  4  2  0  0 | * 8  *  *  *
xo .. ox ..&#x      4 |  2  0  0  4 |  0  0  0  4  0 | * * 16  *  *
xo .. .. xx&#x  &   6 |  2  1  2  4 |  1  0  0  2  2 | * *  * 32  *
.. xx .. xx&#x      8 |  0  4  4  4 |  0  2  0  0  4 | * *  *  * 16

wxxx xwxx xxwx xxxw&#zx   → height = 0
(tegum sum of 4 orthogonal (w,x,x,x)-teses.)

o... o... o... o...     & | 64 |  3  3 |  3  6  3 | 1  3  3  1
--------------------------+----+-------+----------+-----------
.... x... .... ....     & |  2 | 96  * |  2  2  0 | 1  1  2  0
oo.. oo.. oo.. oo..&#x  & |  2 |  * 96 |  0  2  2 | 0  2  1  1
--------------------------+----+-------+----------+-----------
.... x... x... ....     & |  4 |  4  0 | 48  *  * | 1  0  1  0
.... x.x. .... ....&#x  & |  4 |  2  2 |  * 96  * | 0  1  1  0
ooo. ooo. ooo. ooo.&#x  & |  3 |  0  3 |  *  * 64 | 0  1  0  1
--------------------------+----+-------+----------+-----------
.... x... x... x...     &   8 | 12  0 |  6  0  0 | 8  *  *  *
.... x.xx .... ....&#x  &   6 |  3  6 |  0  3  2 | * 32  *  *
.... x..x x..x ....&#x  &   8 |  8  4 |  2  4  0 | *  * 24  *
oooo oooo oooo oooo&#x      4 |  0  6 |  0  0  4 | *  *  * 16

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