Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,5}

Atlas Canonical Name {8,5}*1280

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,1116393)
Rank
3
Schläfli Type
{8,5}
Vertices, edges, …
128, 320, 80
Order of s0s1s2
20
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

64-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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