Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,7}

Atlas Canonical Name {8,7}*1792d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1792,1083551)
Rank
3
Schläfli Type
{8,7}
Vertices, edges, …
128, 448, 112
Order of s0s1s2
7
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 2

56 facets

64 vertex figures

P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 2

56 facets

64 vertex figures

P/N, where N=<s0*(s2*s1)^3*s0*s1*s0*(s2*s1)^2*s2> of order 2

56 facets

64 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 4

28 facets

32 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4

28 facets

32 vertex figures

P/N, where N=<s0*(s2*s1)^3*s0*s1*s0*(s2*s1)^2*s2, s1*s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1> of order 4

28 facets

32 vertex figures

P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4

28 facets

32 vertex figures

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*(s2*s1)^3*s0*s1*s0*(s2*s1)^2*s2> of order 4

28 facets

32 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8

14 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  1, 23)(  2, 24)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 17)(  8, 18)(  9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)( 16, 25)( 33, 55)( 34, 56)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 49)( 40, 50)( 41, 64)( 42, 63)( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 65, 87)( 66, 88)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 81)( 72, 82)( 73, 96)( 74, 95)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 90)( 80, 89)( 97,119)( 98,120)( 99,118)(100,117)(101,116)(102,115)(103,113)(104,114)(105,128)(106,127)(107,125)(108,126)(109,123)(110,124)(111,122)(112,121);;
s1 := (  3, 81)(  4, 82)(  5, 49)(  6, 50)(  7, 97)(  8, 98)(  9, 17)( 10, 18)( 11, 65)( 12, 66)( 13, 33)( 14, 34)( 15,113)( 16,114)( 19, 90)( 20, 89)( 21, 58)( 22, 57)( 23,105)( 24,106)( 25, 26)( 27, 73)( 28, 74)( 29, 41)( 30, 42)( 31,122)( 32,121)( 35, 94)( 36, 93)( 37, 61)( 38, 62)( 39,110)( 40,109)( 43, 78)( 44, 77)( 47,126)( 48,125)( 51, 85)( 52, 86)( 53, 54)( 55,102)( 56,101)( 59, 70)( 60, 69)( 63,117)( 64,118)( 67, 91)( 68, 92)( 71,108)( 72,107)( 79,124)( 80,123)( 83, 84)( 87,100)( 88, 99)( 95,115)( 96,116)(111,119)(112,120)(127,128);;
s2 := (  1, 48)(  2, 47)(  3,112)(  4,111)(  5,128)(  6,127)(  7, 64)(  8, 63)(  9, 32)( 10, 31)( 11, 96)( 12, 95)( 13, 80)( 14, 79)( 15, 16)( 17, 41)( 18, 42)( 19,106)( 20,105)( 21,122)( 22,121)( 23, 57)( 24, 58)( 25, 26)( 27, 89)( 28, 90)( 29, 73)( 30, 74)( 35, 98)( 36, 97)( 37,113)( 38,114)( 39, 50)( 40, 49)( 43, 82)( 44, 81)( 45, 65)( 46, 66)( 51,104)( 52,103)( 53,119)( 54,120)( 59, 87)( 60, 88)( 61, 72)( 62, 71)( 67,109)( 68,110)( 69,126)( 70,125)( 75, 93)( 76, 94)( 77, 78)( 83,107)( 84,108)( 85,124)( 86,123)( 91, 92)(101,115)(102,116);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(128)!(  1, 23)(  2, 24)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 17)(  8, 18)(  9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)( 16, 25)( 33, 55)( 34, 56)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 49)( 40, 50)( 41, 64)( 42, 63)( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 65, 87)( 66, 88)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 81)( 72, 82)( 73, 96)( 74, 95)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 90)( 80, 89)( 97,119)( 98,120)( 99,118)(100,117)(101,116)(102,115)(103,113)(104,114)(105,128)(106,127)(107,125)(108,126)(109,123)(110,124)(111,122)(112,121);
s1 := Sym(128)!(  3, 81)(  4, 82)(  5, 49)(  6, 50)(  7, 97)(  8, 98)(  9, 17)( 10, 18)( 11, 65)( 12, 66)( 13, 33)( 14, 34)( 15,113)( 16,114)( 19, 90)( 20, 89)( 21, 58)( 22, 57)( 23,105)( 24,106)( 25, 26)( 27, 73)( 28, 74)( 29, 41)( 30, 42)( 31,122)( 32,121)( 35, 94)( 36, 93)( 37, 61)( 38, 62)( 39,110)( 40,109)( 43, 78)( 44, 77)( 47,126)( 48,125)( 51, 85)( 52, 86)( 53, 54)( 55,102)( 56,101)( 59, 70)( 60, 69)( 63,117)( 64,118)( 67, 91)( 68, 92)( 71,108)( 72,107)( 79,124)( 80,123)( 83, 84)( 87,100)( 88, 99)( 95,115)( 96,116)(111,119)(112,120)(127,128);
s2 := Sym(128)!(  1, 48)(  2, 47)(  3,112)(  4,111)(  5,128)(  6,127)(  7, 64)(  8, 63)(  9, 32)( 10, 31)( 11, 96)( 12, 95)( 13, 80)( 14, 79)( 15, 16)( 17, 41)( 18, 42)( 19,106)( 20,105)( 21,122)( 22,121)( 23, 57)( 24, 58)( 25, 26)( 27, 89)( 28, 90)( 29, 73)( 30, 74)( 35, 98)( 36, 97)( 37,113)( 38,114)( 39, 50)( 40, 49)( 43, 82)( 44, 81)( 45, 65)( 46, 66)( 51,104)( 52,103)( 53,119)( 54,120)( 59, 87)( 60, 88)( 61, 72)( 62, 71)( 67,109)( 68,110)( 69,126)( 70,125)( 75, 93)( 76, 94)( 77, 78)( 83,107)( 84,108)( 85,124)( 86,123)( 91, 92)(101,115)(102,116);
poly := sub<Sym(128)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle