Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,11,22,2}

Atlas Canonical Name {2,11,22,2}*1936

Overview

Group
SmallGroup(1936,164)
Rank
5
Schläfli Type
{2,11,22,2}
Vertices, edges, …
2, 11, 121, 22, 2
Order of s0s1s2s3s4
22
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

11-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14,113)( 15,123)( 16,122)( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)( 48, 90)( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70);;
s2 := (  3, 15)(  4, 14)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 25,114)( 26,113)( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)( 34,116)( 35,115)( 36,103)( 37,102)( 38,112)( 39,111)( 40,110)( 41,109)( 42,108)( 43,107)( 44,106)( 45,105)( 46,104)( 47, 92)( 48, 91)( 49,101)( 50,100)( 51, 99)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 93)( 58, 81)( 59, 80)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 82)( 69, 70)( 71, 79)( 72, 78)( 73, 77)( 74, 76);;
s3 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119);;
s4 := (124,125);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(125)!(1,2);
s1 := Sym(125)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14,113)( 15,123)( 16,122)( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)( 48, 90)( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70);
s2 := Sym(125)!(  3, 15)(  4, 14)(  5, 24)(  6, 23)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 25,114)( 26,113)( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)( 34,116)( 35,115)( 36,103)( 37,102)( 38,112)( 39,111)( 40,110)( 41,109)( 42,108)( 43,107)( 44,106)( 45,105)( 46,104)( 47, 92)( 48, 91)( 49,101)( 50,100)( 51, 99)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 93)( 58, 81)( 59, 80)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 82)( 69, 70)( 71, 79)( 72, 78)( 73, 77)( 74, 76);
s3 := Sym(125)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119);
s4 := Sym(125)!(124,125);
poly := sub<Sym(125)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;