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Bistratic Lace Towers

Lace towers are defined to be stacks of lace prisms, therefore bistratic lace towers are polytopes with exactly 3 vertex layers aligned atop of each other, which all share a common Coxeter symmetry. It shall be pointed out that lace prisms generally allow to consider different edge length symbols. But in this page we restrict to bistratic CRF lace towers, i.e. which have unit edges only and furthermore their 2D faces are considered to be regular. Therefore non-unit edges only can occur as false ones within the medial layer, connecting 2 coplanar lacing faces of the respective segments.

2D

3D

4D

For comparision purposes in the following listings those will be oriented such that the top circumradius is smaller or at most equal to the bottom one. Furthermore, when equal, that the height(1,2) is smaller or equal to the height(2,3). Also, whenever the across symmetry or a reducible part of it has an additional symmetry of its Dynkin symbol, then it will be oriented within lower lexicographic order, except that mere Stott expansion are aligned, i.e. that ooo and xxx are given the same spott, in fact the lexicographical place of the latter one. The same also is used generally for oAo and xBx, when A is any specific edge or pseudo edge length and B = A+x. (For more clarity on the according groupings the first column in each table is added to provide a visually attracting corresponding logical paranthesis.)

In the following lists only axial (external) blends are explicitely mentioned in the remarks columns, as these thus happen to be "mere" axial stacks. None the less, those casually may happen to be special when some of the lacing facets become collinaer / coplanar / corealmic / ... and thus can be considered to be blended in turn. In case this then could be seen in the equatorial dihedral angles column.


---- 2D (up) ----

A1 across symmetry

Here we have just 3 cases:

Stott Type Lace Tower Polygon Remarks Equatorial Dihedral Angles
 
oqo&#xt
{4} both heights = 1/sqrt(2) = 0.707107
q = sqrt(2) = 1.414214
90°
 
ofx&#xt
{5} height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
f = (1+sqrt(5))/2 = 1.618034
108°
 
xux&#xt
{6} both heights = sqrt(3)/2 = 0.866025
u = 2
120°


---- 3D (up) ----

A2 across symmetry

Here the enumeration is obvious. We just have to select the bistratic Johnson solids with trigonal axial symmetry.

Stott Type Lace Tower Polyhedron Remarks Equatorial Dihedral Angles
 
oox3xux&#xt
tut   (across u) = 180° resulting in lacing {6}
 
oxo3ooo&#xt
tridpy (J12) blend of 2 tets at {3}-{3} = arccos(-7/9) = 141.057559°
oxo3xxx&#xt
tobcu (J27) blend of 2 tricues at {3}-{3} = arccos(-7/9) = 141.057559°
at {4}-{4} = arccos(-1/3) = 109.471221°
 
oxx3xxo&#xt
co blend of 2 gyrated tricues at {3}-{4} = arccos(-1/sqrt(3)) = 125.264390°
 
oxx3ooo&#xt
etripy (J7) blend of tet and trip at {3}-{4} = arccos(-sqrt[8/9]) = 160.528779°
oxx3xxx&#xt
etcu (J18) blend of tricu and hip at {3}-{4} = arccos(-sqrt(8/9)) = 160.528779°
at {4}-{4} = arccos(-sqrt[2/3]) = 144.735610°
 
ofx3xoo&#xt
teddi (J63)   (across f) = 180° resulting in lacing {5}
 
oAo3xox&#xt
tautip (J51) A = (1+sqrt(6))/2 = 1.724745 -
xBx3xox&#xt
tauhip (J57) B = (3+sqrt(6))/2 = 2.724745 -
 
oxo6sox&#xt
gyetcu (J22) blend of tricu and hap at {3}-{3} ≈ 169.428208°
at {3}-{4} ≈ 153.635039°

C2 across symmetry

Here the enumeration is obvious. We just have to select the bistratic Johnson solids with tetragonal axial symmetry.

Stott Type Lace Tower Polyhedron Remarks Equatorial Dihedral Angles
 
oox4oxo&#xt
gyesp (J10) blend of squippy and squap at {3}-{3} ≈ 158.571770°
 
oxo4ooo&#xt
oct blend of 2 squippies at {3}-{3} = arccos(-1/3) = 109.471221°
oxo4xxx&#xt
squobcu (J28) blend of 2 squacues at {3}-{3} = arccos(-1/3) = 109.471221°
at {4}-{4} = 90°
 
oxx4xxo&#xt
squigybcu (J29) blend of 2 gyrated squacues at {3}-{4} = arccos(-sqrt[(3-2 sqrt(2))/6]) = 99.735610°
 
oxx4ooo&#xt
esquipy (J8) blend of squippy and cube at {3}-{4} = arccos(-sqrt(2/3)) = 144.735610°
oxx4xxx&#xt
escu (J19) blend of squacu and op at {3}-{4} = arccos(-sqrt(2/3)) = 144.735610°
at {4}-{4} = 135°
 
oqo4xox&#xt
co   at {3}-{4} = arccos(-1/sqrt(3)) = 125.264390°
 
oxo8sox&#xt
gyescu (J23) blend of squacu and oap at {3}-{3} ≈ 151.330128°
at {3}-{4} ≈ 141.594518°

H2 across symmetry

Here the enumeration is obvious. We just have to select the bistratic Johnson solids with pentagonal axial symmetry.

Stott Type Lace Tower Polyhedron Remarks Equatorial Dihedral Angles
 
oox5oxo&#xt
gyepip (J11) blend of peppy and pap at {3}-{3} = arccos(-sqrt(5)/3) = 138.189685°
 
oxo5ooo&#xt
pedpy (J13) blend of 2 peppies at {3}-{3} = arccos[(4 sqrt(5)-5)/15] = 74.754736°
oxo5xxx&#xt
pobcu (J30) blend of 2 pecues at {3}-{3} = arccos[(4 sqrt(5)-5)/15] = 74.754736°
at {4}-{4} = arccos(1/sqrt(5)) = 63.434949°
 
oxx5xxo&#xt
pegybcu (J31) blend of 2 gyrated pecues at {3}-{4} = arccos(sqrt[(3-sqrt(5))/6]) = 69.094843°
 
oxx5ooo&#xt
epeppy (J9) blend of peppy and pip at {3}-{4} = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368°
oxx5xxx&#xt
epcu (J20) blend of pecu and dip at {3}-{4} = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368°
at {4}-{4} = arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°
 
ofx5xox&#xt
pero (J6)   (across f) = 180° resulting in lacing {5}
 
oxo10sox&#xt
gyepcu (J24) blend of pecu and dap at {3}-{3} ≈ 132.624012°
at {3}-{4} ≈ 126.964118°

A1×A1 across symmetry

Here the enumeration is obvious. We just have to select the bistratic Johnson solids with rectangular axial symmetry. And the prisms of the subdimensional case, for sure.

Stott Type Lace Tower Polyhedron Remarks Equatorial Dihedral Angles
 
oox oyo&#xt
tridpy (J12) y = sqrt(8/3) = 1.632993 -
oox xYx&#xt
etidpy (J14) Y = sqrt[(11+4 sqrt(6))/3] = 2.632993 -
 
oxo oxo&#xt
oct blend of 2 squippies at {3}-{3} = arccos(-1/3) = 109.471221°
 
oxo oxx&#xt
autip (J49) blend of squippy and trip at {3}-{3} = arccos[-sqrt(2/3)] = 144.735610°
at {3}-{4} = arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610°
 
oxx xxo&#xt
gybef (J26) blend of 2 gyrated trips at {3}-{4} = 150°
 
oqo xxx&#xt
cube   at {4}-{4} = 90°
 
ofx xxx&#xt
pip   at {4}-{4} = 108°
 
oAx xox&#xt
bautip (J50) A = (1+sqrt(6))/2 = 1.724745 -
 
xox oqo&#xt
oct   -
xox xwx&#xt
esquidpy (J15)   -
 
xux xxx&#xt
hip   at {4}-{4} = 120°
 
o(qo)o o(oq)o&#xt
oct blend of 2 squippies at {3}-{3} = arccos(-1/3) = 109.471221°
o(qo)o x(xw)x&#xt
esquidpy (J15)   at {3}-{3} = arccos(-1/3) = 109.471221°
at {4}-{4} = 90°
x(wx)x x(xw)x&#xt
squobcu (J28) blend of 2 gyrated squacues at {3}-{3} = arccos(-1/3) = 109.471221°
at {4}-{4} = 90°
 
(xu)o(xu) (ho)B(ho)&#xt
pabauhip (J55) B = sqrt(3)+sqrt(2) = 3.146264 -


---- 4D (up) ----

A3 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oox3oxo3ooo&#xt
aurap blend of octpy and rap at tet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512°
at tet-{3}-oct = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
oox3oxo3xxx&#xt
arse aurap blend of tetatut and coatut at tricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512°
at oct-{3}-tet = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
 
oox3xxo3oxx&#xt
srip blend of octatut and coatut at tricu-{6}-tricu = 180° resulting in lacing co
at trip-{3}-oct = arccos(-sqrt[3/8]) = 127.761244°
 
oox3xfo3oox&#xt
octu   (across o3f .) = 180° resulting in lacing teddi
(across . f3o) = 180° resulting in lacing teddi
 
oox3xux3oox&#xt
octum   (across o3u .) = 180° resulting in lacing tut
(across . u3o) = 180° resulting in lacing tut
 
oox3xux3xoo&#xt
deca   (across o3u .) = 180° resulting in lacing tut
(across . u3o) = 180° resulting in lacing tut
 
oxo3xox3oxo&#xt
ico blend of 2 octacoes at squippy-{4}-squippy = 180° resulting in lacing oct
at oct-{3}-oct = 120°
 
oxo3oox3xxo&#xt
tetacoaoct blend of tetaco and octaco at squippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157°
at oct-{3}-tet = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
at oct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
 
oxo3ooo3ooo&#xt
tete blend of 2 pens at tet-{3}-tet = arccos(-7/8) = 151.044976°
oxo3ooo3xxx&#xt
gyspid blend of 2 tetacoes at tet-{3}-tet = arccos(-7/8) = 151.044976°
at trip-{4}-trip = arccos(-2/3) = 131.810315°
at trip-{3}-trip = arccos(-1/4) = 104.477512°
oxo3xxx3ooo&#xt
octatutbicu blend of 2 octatuts at tricu-{6}-tricu = arccos(-7/8) = 151.044976°
at trip-{3}-trip = arccos(-1/4) = 104.477512°
oxo3xxx3xxx&#xt
tutatobcu blend of tutatoes at tricu-{6}-tricu = arccos(-7/8) = 151.044976°
at trip-{4}-trip = arccos(-2/3) = 131.810315°
at hip-{6}-hip = arccos(-1/4) = 104.477512°
 
oxx3oox3xxo&#xt
tetaco altut blend of tetaco and gyrated coatut at trip-{4}-trip = 180° resulting in lacing gybef
at oct-{3}-trip = arccos(-sqrt[27/32]) = 156.716268°
at tet-{3}-tricu = arccos(-7/8) = 151.044976°
 
oxx3xoo3oxx&#xt
eoctaco blend of octaco and cope at cube-{4}-squippy = 180° resulting in lacing esquipy
at oct-{3}-trip = 150°
 
oxx3ooo3xxo&#xt
spid blend of 2 gyrated tetacoes at trip-{4}-trip = arccos(-2/3) = 131.810315°
at tet-{3}-trip = arccos(-sqrt(3/8)) = 127.761244°
oxx3xxx3xxo&#xt
tutato gybcu blend of 2 gyrated tutatoes at trip-{4}-trip = arccos(-2/3) = 131.810315°
at hip-{6}-tricu = arccos(-sqrt(3/8)) = 127.761244°
 
oxx3ooo3ooo&#xt
etepy blend of pen and tepe at tet-{3}-trip = arccos[-sqrt(15)/4] = 165.522488°
oxx3ooo3xxx&#xt
etetaco blend of tetaco and cope at tet-{3}-trip = arccos[-sqrt(15)/4] = 165.522488°
at cube-{4}-trip = arccos[-sqrt(5/6)] = 155.905157°
at trip-{3}-trip = arccos[-sqrt(5/8)] = 142.238756°
oxx3xxx3ooo&#xt
eoctatut blend of octatut and tuttip at hip-{6}-tricu = arccos[-sqrt(15)/4] = 165.522488°
at trip-{3}-trip = arccos[-sqrt(5/8)] = 142.238756°
oxx3xxx3xxx&#xt
etutatoe blend of tutatoe and tope at hip-{6}-tricu = arccos[-sqrt(15)/4] = 165.522488°
at cube-{4}-trip = arccos[-sqrt(5/6)] = 155.905157°
at hip-{6}-hip = arccos[-sqrt(5/8)] = 142.238756°
 
xxo3oxx3ooo&#xt
tetatutaoct blend of tetatut and octatut at tricu-{6}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
at tet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
xxo3oxx3xxx&#xt
coatoatut blend of coatoe and tutatoe at tricu-{6}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
at hip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
at cube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157°
 
ooo3oxo3ooo&#xt
hex blend of 2 octpies at tet-{3}-tet = 120°
ooo3oxo3xxx&#xt
tetatut bicu blend of 2 tetatuts at tet-{3}-tet = 120°
at tricu-{6}-tricu = 120°
xxx3oxo3xxx&#xt
coatobcu blend of 2 coatoes at tricu-{6}-tricu = 120°
at cube-{4}-cube = 90°
 
ooo3oxx3ooo&#xt
eoctpy blend of octpy and ope at tet-{3}-trip = 150°
ooo3oxx3xxx&#xt
etetatut blend of tetatut and tuttip at tet-{3}-trip = 150°
at tricu-{6}-hip = 150°
xxx3oxx3xxx&#xt
ecoatoe blend of coatoe and tope at hip-{6}-tricu = 150°
at cube-{4}-cube = 135°
 
xfo3oox3ooo&#xt
tetu   (across f3o .) = 180° resulting in lacing teddi
xfo3oox3xxx&#xt
coatutu   (across f3o .) = 180° resulting in lacing teddi
(across f . x) = 180° resulting in lacing pip
at tet-{3}-tricu = arccos[-sqrt(3/32) (sqrt(5)-1)] = 112.238756°
 
oao3xox3ooo&#xt
tau ope a = (2+sqrt(10))/3 = 1.720759 -
oao3xox3xxx&#xt
tehipau tuttip a = (2+sqrt(10))/3 = 1.720759 at tricu-{3}-tricu = arccos(1/4) = 75.522488°
xbx3xox3ooo&#xt
tetripau tuttip b = (5+sqrt(10))/3 = 2.720759 -
xbx3xox3xxx&#xt
tautope b = (5+sqrt(10))/3 = 2.720759 at tricu-{3}-tricu = arccos(1/4) = 75.522488°
 
xux3oox3ooo&#xt
tip   (across u3o .) = 180° resulting in lacing tut
xux3oox3xxx&#xt
coatotum   (across u3o .) = 180° resulting in lacing tut
(across u . x) = 180° resulting in lacing hip
at tet-{3}-tricu = arccos(-sqrt[3/8]) = 127.761244°
...

C3 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oox3ooo4oxo&#xt
ptacubaoct blend of cubpy and octacube at squippy-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[2 sqrt(2)-1])/2] = 152.031248°
oox3xxx4oxo&#xt
coaticatoe blend of coatic and toatic at squacu-{8}-squacu = arccos[-(sqrt(2)-1+sqrt[2 sqrt(2)-1])/2] = 152.031248°
at tricu-{3}-trip = arccos[(3 sqrt(6)-2 sqrt(3)-sqrt[12 sqrt(2)-6])/8] = 85.898535°
 
oox3ooo4oxx&#xt
biscpoxic blend of cubpy and cubasirco at cube-{4}-squippy = 180° resulting in lacing esquipy
oox3xxx4oxx&#xt
biscsrico blend of octatic and ticagirco at op-{8}-squacu = 180° resulting in lacing escu
at tricu-{3}-trip = 150°
 
oxo3oox4xxo&#xt
cubasircoaco blend of cubasirco and coasirco at squippy-{4}-trip = arccos[-(1-sqrt(2)+sqrt[4 sqrt(2)-2])/sqrt(6)] = 127.704362°
at oct-{3}-tet = arccos[-(2-3 sqrt(2)+3 sqrt[4 sqrt(2)-2])/8] = 115.898535°
at cube-{4}-squap = arccos[-(sqrt[2 sqrt(2)-1]-1)/sqrt(sqrt(32))] = 98.515624°
 
oxo3ooo4ooo&#xt
hex blend of 2 octpies at tet-{3}-tet = 120°
oxo3ooo4xxx&#xt
pacsid pith blend of 2 cubasircoes at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
oxo3xxx4ooo&#xt
coatobcu blend of 2 coatoes at tricu-{6}-tricu = 120°
at cube-{4}-cube = 90°
oxo3xxx4xxx&#xt
tica gircobcu blend of 2 ticagircoes at tricu-{6}-tricu = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at op-{8}-op = 90°
 
oxx3oox4xxo&#xt
cubasircoatoe blend of cubasirco and sircoatoe at trip-{4}-trip = arccos[-(2-sqrt(2)+sqrt[8 sqrt(2)-6])/3] = 164.503097°
at tet-{3}-tricu = arccos[-(2 sqrt(2)-3+3 sqrt[4 sqrt(2)-3])/sqrt(32)] = 146.522293°
at cube-{4}-squap = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/sqrt(sqrt(32))] = 149.258250°
 
oxx3xxo4oox&#xt
coatoa sirco blend of coatoe and sircoatoe at tricu-{6}-tricu = arccos[-(3-2 sqrt(2)+3 sqrt[4 sqrt(2)-3])/sqrt(32)] = 153.477707°
at cube-{4}-squap = arccos[-(1-sqrt(2)+sqrt[4 sqrt(2)-3])/sqrt(sqrt(32))] = 120.741750°
 
oxx3ooo4ooo&#xt
eoctpy blend of octpy and ope at tet-{3}-trip = 150°
oxx3ooo4xxx&#xt
ecuba sirco blend of cubasirco and sircope at tet-{3}-trip = 150°
at cube-{4}-trip = arccos(-sqrt[2/3]) = 144.735610°
at cube-{4}-cube = 135°
oxx3xxx4ooo&#xt
ecoatoe blend of coatoe and tope at hip-{6}-tricu = 150°
at cube-{4}-cube = 135°
oxx3xxx4xxx&#xt
etica girco blend of ticagirco and gircope at hip-{6}-tricu = 150°
at cube-{4}-trip = arccos(-sqrt[2/3]) = 144.735610°
at op-{8}-op = 135°
 
xoo3oxo4oox&#xt
octacoacube blend of octaco and cubaco at squap-{4}-squippy = arccos[-sqrt(8-3 sqrt(2))/2] = 165.741750°
at oct-{3}-tet = arccos[-(3-sqrt(8)+3 sqrt[4 sqrt(2)-3])/(4 sqrt(2))] = 153.477707°
 
xoo3oxx4ooo&#xt
eoctaco blend of octaco and cope at cube-{4}-squippy = 180° resulting in lacing esquipy
at oct-{3}-trip = 150°
xoo3oxx4xxx&#xt
esircoatic blend of sircoatic and ticcup at op-{8}-squacu = 180° resulting in lacing escu
at oct-{3}-trip = 150°
 
xox3oxo4ooo&#xt
ico blend of 2 octacoes at squippy-{4}-squippy = 180° resulting in lacing oct
at oct-{3}-oct = 120°
xox3oxo4xxx&#xt
pacsrit blend of 2 sircoatics at squacu-{8}-squacu = 180° resulting in lacing squobcu
at oct-{3}-oct = 120°
 
xxo3oox4oxo&#xt
octasircoaco blend of octasirco and coasirco at squippy-{4}-trip = arccos[-(2-2 sqrt(2)+sqrt[4 sqrt(2)-2])/sqrt(12)] = 108.233141°
at squap-{4}-squippy = arccos[-(sqrt[2 sqrt(2)-1]-1)/sqrt(sqrt(32))] = 98.515624°
at oct-{3}-trip = arccos[sqrt(3) (3 sqrt(2)-2-sqrt[4 sqrt(2)-2])/8] = 85.898535°
 
xxo3oox4oxx&#xt
octasircoatic blend of octasirco and sircoatic at trip-{4}-trip = arccos(-sqrt[8/9]) = 160.528779°
at oct-{3}-trip = 150°
at squacu-{4}-squippy = 135°
 
xxo3ooo4oxx&#xt
octasircoacube blend of octasirco and cubasirco at cube-{4}-squippy = 90°
at tet-{3}-trip = 90°
at trip-{4}-trip = 90°
xxo3xxx4oxx&#xt
toagircoatic blend of toagirco and ticagirco at hip-{6}-tricu = 90°
at op-{8}-squacu = 90°
at trip-{4}-trip = 90°
 
ooo3oox4oxo&#xt
ptacubaco blend of cubpy and cubaco at squap-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/(2 sqrt[sqrt(2)])] = 149.258250°
xxx3oox4oxo&#xt
octasircoatoe blend of octasirco and sircoatoe at tricu-{3}-trip = arccos[-(2 sqrt(6)-sqrt(3)+sqrt[12 sqrt(2)-9])/(4 sqrt[sqrt(8)])] = 152.928678°
at squap-{4}-squippy = arccos[-(sqrt(2)-1+sqrt[4 sqrt(2)-3])/(2 sqrt[sqrt(2)])] = 149.258250°
at trip-{4}-trip = arccos[-(2 sqrt(2)-2+sqrt[4 sqrt(2)-3])/3] = 145.031877°
 
ooo3xox4oqo&#xt
rit   (across . o4q) = 180° resulting in lacing co
xxx3xox4oqo&#xt
pabdirico   at tricu-{3}-tricu = 120°
(across x . q) = 180° resulting in lacing cube
(across . o4q) = 180° resulting in lacing co
 
ooo3ooo4oxo&#xt
cute blend of 2 cubpies at squippy-{4}-squippy = 90°
ooo3xxx4oxo&#xt
coaticbicu blend of 2 coatics at squacu-{8}-squacu = 90°
at trip-{3}-trip = 60°
xxx3ooo4oxo&#xt
octa sircobcu blend of 2 octasircoes at squippy-{4}-squippy = 90°
at trip-{4}-trip = arccos(1/3) = 70.528779°
at trip-{3}-trip = 60°
xxx3xxx4oxo&#xt
toagircobcu blend of 2 toagircoes at squacu-{8}-squacu = 90°
at trip-{4}-trip = arccos(1/3) = 70.528779°
at hip-{6}-hip = 60°
 
ooo3ooo4oxx&#xt
ecubpy blend of cubpy and tes at cube-{4}-squippy = 135°
ooo3xxx4oxx&#xt
ecoatic blend of coatic and ticcup at op-{8}-squacu = 135°
at trip-{3}-trip = 120°
xxx3ooo3oxx&#xt
eocta sirco blend of octasirco and sircope at cube-{4}-squippy = 135°
at cube-{4}-trip = arccos(-1/sqrt(3)) = 125.264390°
at trip-{3}-trip = 120°
xxx3xxx4oxx&#xt
etoa girco blend of toagirco and gircope at op-{8}-squacu = 135°
at cube-{4}-trip = arccos(-1/sqrt(3)) = 125.264390°
at hip-{6}-hip = 120°
 
xfo3oox4ooo&#xt
octu   (across o3f .) = 180° resulting in lacing teddi
xfo3oox4xxx&#xt
sirco aticu   (across f3o .) = 180° resulting in lacing teddi
(across f . x) = 180° resulting in lacing pip
 
xux3oox4ooo&#xt
octum   (across u3o .) = 180° resulting in lacing tut
xux3oox4xxx&#xt
sircoa gircotum   (across u3o .) = 180° resulting in lacing tut
(across u . x) = 180° resulting in lacing hip
at cube-{4}-squacu = 135°
 
oqo3ooo4xox&#xt
pabdico   -
oqo3xxx4xox&#xt
dapabdi spic   at squacu-{4}-squacu = 90°
xwx3ooo4xox&#xt
dapabdi poxic   -
xwx3xxx4xox&#xt
hagy gircope   at squacu-{4}-squacu = 90°
 
oao3xox4ooo&#xt
haucope a = 1+1/sqrt(2) = 1.707107 -
oao3xox4xxx&#xt
hau ticcup a = 1+1/sqrt(2) = 1.707107 at squacu-{4}-squacu = 90°
xbx3xox4ooo&#xt
hautope b = 2+1/sqrt(2) = 2.707107 -
xbx3xox4xxx&#xt
hau gircope b = 2+1/sqrt(2) = 2.707107 at squacu-{4}-squacu = 90°
 
oos3oos4oxo&#xt
pta cubaike blend of cubpy and cubaike at squippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157°
 
oso3oso4oox&#xt
ptaika cube blend of ikepy and cubaike at tet-{3}-tet = 120°
at squippy-{3}-tet = arccos(-1/4) = 104.477512°
...

H3 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oxo3ooo5oox&#xt
biscex blend of ikepy and ikadoe at tet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512°
oxo3xxx5oox&#xt
idatiatid blend of idati and tiatid at tricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512°
at pecu-{5}-pip = 126°
 
oxo3oox5xxo&#xt
doasridaid blend of doasrid and idasrid at squippy-{4}-trip = arccos(1/sqrt(6)) = 65.905157°
at oct-{3}-tet = 60°
at pap-{5}-pip = 54°
 
oxo3xox5oxo&#xt
idasrid bicu blend of 2 idasrids at squippy-{4}-squippy = 90°
at oct-{3}-oct = arccos(1/4) = 75.522488°
at pap-{5}-pap = 72°
 
oxo3ooo5ooo&#xt
it blend of 2 ikepies at tet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512°
oxo3ooo5xxx&#xt
doasrid bicu blend of 2 doasrids at tet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512°
at trip-{4}-trip = arccos(sqrt(5)/3) = 41.810315°
at pip-{5}-pip = 36°
oxo3xxx5ooo&#xt
idatibcu blend of 2 idatis at tricu-{6}-tricu = arccos[(3 sqrt(5)-1)/8] = 44.477512°
at pip-{5}-pip = 36°
oxo3xxx5xxx&#xt
tidagrid bicu blend of 2 tidagrids at tricu-{6}-tricu = arccos[(3 sqrt(5)-1)/8] = 44.477512°
at trip-{4}-trip = arccos(sqrt(5)/3) = 41.810315°
at dip-{10}-dip = 36°
 
oxx3xoo5oxx&#xt
eidasrid blend of idasrid and sriddip at cube-{4}-squippy = 135°
at oct-{3}-trip = arccos(-sqrt[3/8]) = 127.761244°
at pap-{5}-pip = 126°
 
oxx3xox5oxo&#xt
idasridati blend of idasrid and sridati at squippy-{4}-trip = arccos[-sqrt(5/6)] = 155.905157°
at pap-{5}-pap = 144°
at oct-{3}-tricu = arccos[-(3 sqrt(5)-1)/8] = 135.522488°
 
oxx3xxo5oox&#xt
idatiasrid blend of idati and sridati at tricu-{6}-tricu = arccos(-1/4) = 104.477512°
at pap-{5}-pip = 90°
 
oxx3ooo5ooo&#xt
eikepy blend of ikepy and ipe at tet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
oxx3ooo5xxx&#xt
edoasrid blend of doasrid and sriddip at tet-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
at cube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157°
at pip-{5}-pip = 108°
oxx3xxx5ooo&#xt
eidati blend of idati and tipe at hip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
at pip-{5}-pip = 108°
oxx3xxx5xxx&#xt
etidagrid blend of tidagrid and griddip at hip-{6}-tricu = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
at cube-{4}-trip = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157°
at dip-{10}-dip = 108°
 
xoo3oox5oxo&#xt
ikadoaid blend of ikadoe and doaid at pap-{5}-peppy = 180° resulting in lacing gyepip
 
xoo3oxo5oox&#xt
ikaidadoe blend of ikaid and doaid at pap-{5}-peppy = 108°
at oct-{3}-tet = arccos(-1/4) = 104.477512°
 
xoo3oxx5ooo&#xt
eikaid blend of ikaid and iddip at pip-{5}-peppy = 126°
at oct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
xoo3oxx5xxx&#xt
esridatid blend of sridatid and tiddip at dip-{10}-pecu = 126°
at oct-{3}-trip = arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
 
xoo3ooo5oxx&#xt
eikadoe blend of ikadoe and dope at pip-{5}-peppy = 162°
xoo3xxx5oxx&#xt
etiatid blend of tiatid and tiddip at dip-{10}-pecu = 162°
at tricu-{3}-trip = arccos(-sqrt[3/8]) = 127.761244°
 
xox3oxo5oox&#xt
biscrox blend of ikaid and idasrid at pap-{5}-peppy = 180° resulting in lacing gyepip
at oct-{3}-oct = arccos[-(1+3 sqrt(5))/8] = 164.477512°
 
xox3oxo5ooo&#xt
ikaidbicu blend of 2 ikaids at peppy-{5}-peppy = 72°
at oct-{3}-oct = arccos[(3 sqrt(5)-1)/8] = 44.477512°
xox3oxo5xxx&#xt
sridatidbicu blend of 2 sridatids at pecu-{10}-pecu = 72°
at oct-{3}-oct = arccos[(3 sqrt(5)-1)/8] = 44.477512°
 
xox3oxx5xxo&#xt
srida tidati blend of sridatid and tiatid at pecu-{10}-pecu = 108°
at oct-{3}-tricu = 60°
 
xox3ooo5oxo&#xt
ikadobcu blend of 2 ikadoes at peppy-{5}-peppy = 144°
xox3xxx5oxo&#xt
tiatidbicu blend of 2 tiatids at pecu-{10}-pecu = 144°
at tricu-{3}-tricu = arccos(1/4) = 75.522488°
 
ooo3oxo5xox&#xt
doaid bicu blend of 2 doaids at tet-{3}-tet = arccos[-(1+3 sqrt(5))/8] = 164.477512°
at pap-{5}-pap = 144°
xxx3oxo5xox&#xt
sridatibcu blend of 2 sridatis at tricu-{6}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512°
at pap-{5}-pap = 144°
 
ooo3oxx5xoo&#xt
edoaid blend of doaid and iddip at tet-{3}-trip = arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756°
at pap-{5}-pip = 162°
xxx3oxx5xoo&#xt
esridati blend of sridati and tipe at hip-{6}-tricu = arccos(-sqrt[9+3 sqrt(5)]/4) = 172.238756°
at pap-{5}-pip = 162°
 
ooo3xox5ofx&#xt
biscrahi   (across . o5f) = 180° resulting in lacing pero
xxx3xox5ofx&#xt
arse biscrahi   (across x . f) = 180° resulting in lacing pip
(across . o5f) = 180° resulting in lacing pero
at tricu-{3}-tricu = arccos[-(1+3 sqrt(5))/8] = 164.477512°
 
xfo3oox5ooo&#xt
iku   (across f3o .) = 180° resulting in lacing teddi
xfo3oox5xxx&#xt
sridatidu   (across f3o .) = 180° resulting in lacing teddi
(across f . x) = 180° resulting in lacing pip
at pecu-{5}-pip = 162°
 
xux3oox5ooo&#xt
iktum   (across u3o .) = 180° resulting in lacing tut
xux3oox5xxx&#xt
srida gridtum   (across u3o .) = 180° resulting in lacing tut
(across u . x) = 180° resulting in lacing hip
at pecu-{5}-pip = 162°
 
oAo3ooo5xox&#xt
owaudope A = 3/sqrt(5) = 1.341641 -
oAo3xxx5xox&#xt
twagy tiddip A = 3/sqrt(5) = 1.341641 at pecu-{5}-pecu = 144°
xBx3ooo5xox&#xt
twau sriddip B = (5+3 sqrt(5))/5 = 2.341641 -
xBx3xxx5xox&#xt
twagy griddip B = (5+3 sqrt(5))/5 = 2.341641 at pecu-{5}-pecu = 144°
 
ofo3oox5xoo&#xt
twau doaid   -
xFx3oox5xoo&#xt
twau sridati   -
 
ofo3xox5ooo&#xt
twau iddip   -
ofo3xox5xxx&#xt
twau tiddip   at pecu-{5}-pecu = 144°
xFx3xox5ooo&#xt
twau tipe   -
xFx3xox5xxx&#xt
twau griddip   at pecu-{5}-pecu = 144°
...

A1×A2 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oxo oox3oxo&#xt
rap blend of trippy and traf at squippy-{4}-squippy = 180° resulting in lacing oct
at oct-{3}-tet = arccos(-1/4) = 104.477512°
 
oxo oxo3ooo&#xt
tript blend of 2 trippies at squippy-{4}-squippy = arccos(-2/3) = 131.810315°
at tet-{3}-tet = arccos(-1/4) = 104.477512°
oxo oxo3xxx&#xt
tripuf bicu blend of 2 tripufs at squippy-{4}-squippy = arccos(-2/3) = 131.810315°
at tricu-{6}-tricu = arccos(-1/4) = 104.477512°
at trip-{4}-trip = arccos(-1/9) = 96.379370°
 
oxx oxx3ooo&#xt
etrippy blend of trippy and tisdip at cube-{4}-squippy = arccos[-sqrt(5/6)] = 155.905157°
at tet-{3}-trip = arccos[-sqrt(5/8)] = 142.238756°
oxx oxx3xxx&#xt
etripuf blend of tripuf and shiddip at cube-{4}-squippy = arccos[-sqrt(5/6)] = 155.905157°
at hip-{6}-tricu = arccos[-sqrt(5/8)] = 142.238756°
at cube-{4}-trip = arccos[-sqrt(5)/3] = 138.189685°
 
oqo oox3xoo&#xt
hex   -
 
oCo ooo3oox&#xt
tete C = sqrt(5/2) = 1.581139 -
oCo xxx3oox&#xt
tracufbil C = sqrt(5/2) = 1.581139 at trip-{3}-tricu = arccos(sqrt[3/8]) = 52.238756°
 
x(ou)x o(xo)x3x(xo)o&#xt
spid   (across (..) (xo)3(..)) = 180° resulting in lacing trip
(across (..) (..)3(xo)) = 180° resulting in lacing trip
 
x(ou)x o(ox)x3x(uo)x&#xt
biscsrip   (across (ou) (..)3(uo)) = 180° resulting in lacing co
(across (..) (ox)3(..)) = 180° resulting in lacing trip
at oct-{3}-tricu = arccos(-1/4) = 104.477512°
 
oso2oso3oso&#xt
hex blend of 2 octpies at tet-{3}-tet = 120°
...
 
oqo xxx3ooo&#xt
tisdip   at trip-{3}-trip = 90°
oqo xxx3xxx&#xt
shiddip   at hip-{6}-hip = 90°
 
ofx xxx3ooo&#xt
trapedip   at trip-{3}-trip = 108°
ofx xxx3xxx&#xt
phiddip   at hip-{6}-hip = 108°
 
xux xxx3ooo&#xt
thiddip   at trip-{3}-trip = 120°
xux xxx3xxx&#xt
hiddip   at hip-{6}-hip = 120°
 
xxx oox3xux&#xt
tuttip   (across x . u) = 180° resulting in lacing hip
(across . o3u) = 180° resulting in lacing tut
 
xxx oxo3ooo&#xt
tridpyp blend of 2 tepes at tet-{3}-tet = 180° resulting in lacing tridpy
at trip-{3}-trip = arccos(-7/9) = 141.057559°
xxx oxo3xxx&#xt
tobcupe blend of 2 tricupes at tricu-{6}-tricu = 180° resulting in lacing tobcu
at trip-{3}-trip = arccos(-7/9) = 141.057559°
at cube-{4}-cube = arccos(-1/3) = 109.471221°
 
xxx oxx3xxo&#xt
cope blend of 2 gyrated tricupes at tricu-{6}-tricu = 180° resulting in lacing co
at cube-{4}-trip = arccos(-1/sqrt(3)) = 125.264390°
 
xxx oxx3ooo&#xt
etepe blend of tepe and tisdip at tet-{3}-trip = 180° resulting in lacing etripy
at cube-{4}-trip = arccos(-sqrt[8/9]) = 160.528779°
xxx oxx3xxx&#xt
etcupe blend of tricupe and shiddip at hip-{6}-tricu = 180° resulting in lacing etcu
at cube-{4}-trip = arccos(-sqrt[8/9]) = 160.528779°
at cube-{4}-cube = arccos(-sqrt[2/3]) = 144.735610°
 
xxx ofx3xoo&#xt
teddipe   (across x f .) = 180° resulting in lacing pip
(across . f3o) = 180° resulting in lacing teddi
 
xxx oAo3xox&#xt
tautipip A = (1+sqrt(6))/2 = 1.724745 -
xxx xBx3xox&#xt
tauhipip B = (3+sqrt(6))/2 = 2.724745 -
 
xxx oxo6sox&#xt
gyetcupe blend of tricupe and happip at hap-{6}-tricu = 180° resulting in lacing gyetcu
at trip-{3}-trip ≈ 169.428208°
at cube-{4}-trip ≈ 153.635039°

A1×C2 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oxo oxo4ooo&#xt
cute blend of 2 cubpies at squippy-{4}-squippy = 90°
oxo oxo4xxx&#xt
squipuf bicu blend of 2 squipuf and tes at squacu-{8}-squacu = 90°
at squippy-{4}-squippy = 90°
at trip-{4}-trip = arccos(1/3) = 70.528779°
 
oyo oox4xoo&#xt
squapt y = sqrt[2-1/sqrt(2)] = 1.137055 -
 
oxx oxx4ooo&#xt
ecubpy blend of cubpy and tes at squippy-{4}-squippy = 135°
oxx oxx4xxx&#xt
esquipuf blend of squipuf and sodip at cube-{4}-squippy = 135°
at op-{8}-squacu = 135°
at cube-{4}-trip = arccos(-1/sqrt(3)) = 125.264390°
 
xox oxo4ooo&#xt
hex   -
xox oxo4xxx&#xt
quawros   -
 
xox xox4oqo&#xt
cytau tes   -
xox xox4xwx&#xt
cyte cubau sodip   -
 
o(qo)o o(ox)o4o(oo)o&#xt
hex blend of 2 octpies at tet-{3}-tet = 120°
o(qo)o o(ox)o4x(xx)x&#xt
quawros blend of 2 squacufbils at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
x(wx)x o(ox)o4o(oo)o&#xt
pex hex blend of 2 esquippidpies at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
x(wx)x o(ox)o4x(xx)x&#xt
pacsid pith blend of 2 cubasircoes at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
 
(qo)q(qo) (ox)x(ox)4(oo)o(oo)&#xt
cytau tes   (across q x .) = 180° resulting in lacing cube
at squippy-{4}-squippy = 180° resulting in lacing oct
(qo)q(qo) (ox)x(ox)4(xx)x(xx)&#xt
cyte opau sodip   (across q x .) = 180° resulting in lacing cube
(across q . x) = 180° resulting in lacing cube
at squacu-{8}-squacu = 180° resulting in lacing squobcu
 
(qo)q(qo) (xo)o(xo)4(oq)q(oq)&#xt
rit   (across . o4q) = 180° resulting in lacing co
 
(qo)(qo)(qo) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt
ico blend of 2 octacoes at squippy-{4}-squippy = 180° resulting in lacing oct
at oct-{3}-oct = 120°
(qo)(qo)(qo) (ox)(xo)(ox)4(xx)(xw)(xx)&#xt
bicyte ausodip   (across (qo) (..) (xw)) = 180° resulting in lacing esquidpy
at squacu-{8}-squacu = 180° resulting in lacing squobcu
at oct-{3}-oct = 120°
(wx)(wx)(wx) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt
pexic   (across (wx) (..) (oq)) = 180° resulting in lacing esquidpy
at squippy-{4}-squippy = 180° resulting in lacing oct
at oct-{3}-oct = 120°
(wx)(wx)(wx) (ox)(xo)(ox)4(xx)(xw)(xx)&#xt
pacsrit blend of 2 sircoatics at squacu-{8}-squacu = 180° resulting in lacing squobcu
at oct-{3}-oct = 120°
 
oso2oso4oso&#xt
squapt blend of 2 squappies at squippy-{4}-squippy = arccos[-(2-sqrt(2))/2] = 107.031248°
at tet-{3}-tet = arccos[(3 sqrt(2)-4)/8] = 88.261948°
...
 
oqo xxx4ooo&#xt
tes   (across q x .) = 180° resulting in lacing cube
at cube-{4}-cube = 90°
oqo xxx4xxx&#xt
sodip   (across q x .) = 180° resulting in lacing cube
(across q . x) = 180° resulting in lacing cube
at op-{8}-op = 90°
 
ofx xxx4ooo&#xt
squipdip   (across f x .) = 180° resulting in lacing pip
at cube-{4}-cube = 108°
ofx xxx4xxx&#xt
podip   (across f x .) = 180° resulting in lacing pip
(across f . x) = 180° resulting in lacing pip
at op-{8}-op = 108°
 
xux xxx4ooo&#xt
shiddip   (across u x .) = 180° resulting in lacing hip
at cube-{4}-cube = 120°
xux xxx4xxx&#xt
hodip   (across u x .) = 180° resulting in lacing hip
(across u . x) = 180° resulting in lacing hip
at op-{8}-op = 120°
 
xxx oox4oxo&#xt
gyespyp blend of squippyp and squappip at squap-{4}-squippy = 180° resulting in lacing gyesp
at trip-{4}-trip ≈ 158.571770°
 
xxx oxo4ooo&#xt
ope blend of 2 squippyps at squippy-{4}-squippy = 180° resulting in lacing oct
at trip-{4}-trip = arccos(-1/3) = 109.471221°
xxx oxo4xxx&#xt
squobcupe blend of 2 squacupes at squacu-{8}-squacu = 180° resulting in lacing squobcu
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
 
xxx oxx4xxo&#xt
squigybcupe blend of 2 gyrated squacupes at squacu-{8}-squacu = 180° resulting in lacing squigybcu
at cube-{4}-trip = arccos(-sqrt[(3-2 sqrt(2))/6]) = 99.735610°
 
xxx oxx4ooo&#xt
esquipyp blend of squippyp and tes at cube-{4}-squippy = 180° resulting in lacing esquipy
at cube-{4}-trip = arccos(-sqrt(2/3)) = 144.735610°
xxx oxx4xxx&#xt
escupe blend of squacupe and sodip at op-{8}-squacu = 180° resulting in lacing escu
at cube-{4}-trip = arccos(-sqrt(2/3)) = 144.735610°
at cube-{4}-cube = 135°
 
xxx oqo4xox&#xt
cope   (across x q .) = 180° resulting in lacing cube
(across . q4o) = 180° resulting in lacing co
 
xxx oxo8sox&#xt
gyescupe blend of squacupe and oappip at oap-{8}-squacu = 180° resulting in lacing gyescu
at trip-{4}-trip ≈ 151.330128°
at cube-{4}-trip ≈ 141.594518°

A1×H2 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
ovo oox5xoo&#xt
papt v = (sqrt(5)-1)/2 = 0.618034 -
 
oxo oxo5ooo&#xt
pipt blend of 2 pippies at peppy-{5}-peppy = 36°
at squippy-{4}-squippy = arccos(2/sqrt(5)) = 26.565051°
oxo oxo5xxx&#xt
pepuf bicu blend of 2 pepufs at pecu-{10}-pecu = 36°
at squippy-{4}-squippy = arccos(2/sqrt(5)) = 26.565051°
at trip-{4}-trip = arccos[(5+4 sqrt(5))/15] = 21.624634°
 
oxx oxx5ooo&#xt
epippy blend of pippy and squipdip at peppy-{5}-pip = 108°
at cube-{4}-squippy = arccos(sqrt[(5-2 sqrt(5))/10]) = 103.282526°°
oxx oxx5xxx&#xt
epepuf blend of pepuf and squadedip at dip-{10}-pecu = 108°
at cube-{4}-squippy = arccos(sqrt[(5-2 sqrt(5))/10]) = 103.282526°
at cube-{4}-trip = arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
 
oso2oso5oso&#xt
papt blend of 2 pappies at peppy-{5}-peppy = 72°
at tet-{3}-tet = arccos[(3 sqrt(5)-1)/8] = 44.477512°
...
 
oqo xxx5ooo&#xt
squipdip   (across q x .) = 180° resulting in lacing cube
at pip-{5}-pip = 90°
oqo xxx5xxx&#xt
squadedip   (across q x .) = 180° resulting in lacing cube
(across q . x) = 180° resulting in lacing cube
at dip-{10}-dip = 90°
 
ofx xxx5ooo&#xt
pedip   (across f x .) = 180° resulting in lacing pip
at pip-{5}-pip = 108°
ofx xxx5xxx&#xt
padedip   (across f x .) = 180° resulting in lacing pip
(across f . x) = 180° resulting in lacing pip
at dip-{10}-dip = 108°
 
xux xxx5ooo&#xt
phiddip   (across u x .) = 180° resulting in lacing hip
at pip-{5}-pip = 120°
xux xxx5xxx&#xt
hadedip   (across u x .) = 180° resulting in lacing hip
(across u . x) = 180° resulting in lacing hip
at dip-{10}-dip = 120°
 
xxx oox5oxo&#xt
gyepippip blend of pippy and pappip at pap-{5}-peppy = 180° resulting in lacing geypip
at trip-{4}-trip = arccos(-sqrt(5)/3) = 138.189685°
 
xxx oxo5ooo&#xt
pedpyp blend of 2 peppyps at peppy-{5}-peppy = 180° resulting in lacing pedpy
at trip-{4}-trip = arccos[(4 sqrt(5)-5)/15] = 74.754736°
xxx oxo5xxx&#xt
pobcupe blend of 2 pecupes at pecu-{10}-pecu = 180° resulting in lacing pobcu
at trip-{4}-trip = arccos[(4 sqrt(5)-5)/15] = 74.754736°
at cube-{4}-cube = arccos(1/sqrt(5)) = 63.434949°
 
xxx oxx5xxo&#xt
pegybcupe blend of 2 gyrated pecupes at pecu-{10}-pecu = 180° resulting in lacing pegybcu
at cube-{4}-trip = arccos(sqrt[(3-sqrt(5))/6]) = 69.094843°
 
xxx oxx5ooo&#xt
epeppyp blend of peppyp and squipdip at peppy-{5}-pip = 180° resulting in lacing epeppy
at cube-{4}-trip = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368°
xxx oxx5xxx&#xt
epcupe blend of pecupe and squadedip at dip-{10}-pecu = 180° resulting in lacing epcu
at cube-{4}-trip = arccos(-sqrt[(10-2 sqrt(5))/15]) = 127.377368°
at cube-{4}-cube = arccos(-sqrt[(5-sqrt(5))/10]) = 121.717474°
 
xxx ofx5xox&#xt
perope   (across x f .) = 180° resulting in lacing pip
(across . f5o) = 180° resulting in lacing pero
 
xxx oxo10sox&#xt
gyepcupe blend of pecupe and dappip at dap-{10}-pecu = 180° resulting in lacing gyepcu
at trip-{4}-trip ≈ 132.624012°
at cube-{4}-trip ≈ 126.964118°

A1×A1×A1 across symmetry

Stott Type Lace Tower Polychoron Remarks Equatorial Dihedral Angles
 
oxo oxo oxo&#xt
cute blend of 2 cubpies at squippy-{4}-squippy = 90°
 
oxo oxo xox&#xt
hex   -
 
oxo xox xox&#xt
cute   -
 
oao oox xoo&#xt
tete a = sqrt(5/2) = 1.581139 -
 
oso2oso2oso&#xt
tete blend of 2 pens at tet-{3}-tet = arccos(-7/8) = 151.044976°
...
 
oox oyo xxx&#xt
tridpyp y = sqrt(8/3) = 1.632993 -
oox xYx xxx&#xt
etidpyp Y = sqrt[(11+4 sqrt(6))/3] = 2.632993 -
 
oxo oxo xxx&#xt
ope blend of 2 squippyps at squippy-{4}-squippy = 180° resulting in lacing oct
at trip-{4}-trip = arccos(-1/3) = 109.471221°
 
oxo oxx xxx&#xt
autipip blend of squippyp and tisdip at squippy-{4}-trip = 180° resulting in lacing autip
at trip-{4}-trip = arccos[-sqrt(2/3)] = 144.735610°
at cube-{4}-trip = arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610°
 
oxx xxo xxx&#xt
gybeffip blend of 2 gyrated tisdips at trip-{4}-trip = 180° resulting in lacing gybef
at cube-{4}-trip = 150°
 
oqo xxx xxx&#xt
tes   (across q x .) = 180° resulting in lacing cube
(across q . x) = 180° resulting in lacing cube
at cube-{4}-cube = 90°
 
ofx xxx xxx&#xt
squipdip   (across f x .) = 180° resulting in lacing pip
(across f . x) = 180° resulting in lacing pip
at cube-{4}-cube = 108°
 
oAx xox xxx&#xt
bautipip A = (1+sqrt(6))/2 = 1.724745 -
 
xox oqo xxx&#xt
ope   -
xox xwx xxx&#xt
esquidpyp   -
 
xux xxx xxx&#xt
shiddip   (across u x .) = 180° resulting in lacing hip
(across u . x) = 180° resulting in lacing hip
at cube-{4}-cube = 120°
 
o(ox)o o(ox)o x(wx)x&#xt
pex hex blend of 2 esquippidpies at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
 
o(qo)o o(oq)o x(xx)x&#xt
ope blend of 2 squippyps at squippy-{4}-squippy = 180° resulting in lacing oct
at trip-{4}-trip = arccos(-1/3) = 109.471221°
o(qo)o x(xw)x x(xx)x&#xt
esquidpyp   (across (qo) (xw) (..)) = 180° resulting in lacing esquidpy
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
x(wx)x x(xw)x x(xx)x&#xt
squobcupe blend of 2 squacupes (across (wx) (xw) (..)) = 180° resulting in lacing squobcu
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
 
o(qoo)o o(oqo)o o(ooq)o&#xt
hex blend of 2 octpies at tet-{3}-tet = 120°
o(qoo)o o(oqo)o x(xxw)x&#xt
pex hex blend of 2 esquippidpies at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
o(qoo)o x(xwx)x x(xxw)x&#xt
quawros blend of 2 squacufbils at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
x(wxx)x x(xwx)x x(xxw)x&#xt
pacsid pith blend of 2 cubasircoes at tet-{3}-tet = 120°
at trip-{4}-trip = arccos(-1/3) = 109.471221°
at cube-{4}-cube = 90°
 
(xu)o(xu) (ho)B(ho) (xx)x(xx)&#xt
pabaushiddip B = sqrt(3)+sqrt(2) = 3.146264 -



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