Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,8}

Atlas Canonical Name {20,8}*1280j

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,1116427)
Rank
3
Schläfli Type
{20,8}
Vertices, edges, …
80, 320, 32
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
  • Self-Petrie

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

References

None.

to this polytope.

Twisty Puzzle