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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 explicitly 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) ----
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) ----
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)/3] = 160.528779° | |
oxx3xxx&#xt | etcu (J18) | blend of tricu and hip |
at {3}-{4} = arccos[-sqrt(8)/3] = 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° |
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° |
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° |
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) ----
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° | ||
xx(qo)3oo(oo)3ox(oq)&#xt | tetacoa cube | blend of tetaco and cubaco |
(across x3o .) = arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864° (across x . x) = arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907° (across . o3x) = arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195° | |
xx(qo)3xx(xx)3ox(oq)&#xt | tutatoa sirco | blend of tutatoe and sircoatoe |
(across x3x .) = arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864° (across x . x) = arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907° (across . x3x) = arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195° | |
... |
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)/3] = 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° | |
... |
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 | ite | 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° | |
xoo3ofx5xox&#xt | ... |
(across o3f .) = 180° resulting in lacing teddi (across . f5o) = 180° resulting in lacing pero | ||
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 | rite | 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° | ||
sys3sos5sos&#xt | twausniddip | y ≈ 2.253679 | - | |
... |
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 oxo3ooo&#xt | autepe | blend of trippy and tepe |
at tet-{3}-tet = arccos[-sqrt(5/8)] = 142.238756° at squippy-{4}-trip = arccos[-sqrt((41-4 sqrt(10))/54)] = 136.433934° | |
oxx oxo3xxx&#xt | triahipatrip | blend of tripuf and tricupe |
at tricu-{6}-tricu = arccos[-sqrt(5/8)] = 142.238756° at squippy-{4}-trip = arccos[-sqrt((41-4 sqrt(10))/54)] = 136.433934° at cube-{4}-trip = arccos[-sqrt((32-21 sqrt(2))/46)] = 102.925295° | |
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° | |
oxx xxo3ooo&#xt | (?) | blend of tepe and triddip |
at trip-{4}-sqtripuippy = arccos[-sqrt(8)/3] = 160.528779° at tet-{3}-trip = 150° | |
oxx xxo3xxx&#xt | (?) | blend of thiddip and tricupe | ... | |
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)/3] = 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)/3] = 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° |
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° |
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° |
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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