Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,20}

Atlas Canonical Name {8,20}*1280k

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,1116427)
Rank
3
Schläfli Type
{8,20}
Vertices, edges, …
32, 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
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

4-fold

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

References

None.

to this polytope.

Twisty Puzzle