Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,36,6,2}

Atlas Canonical Name {2,36,6,2}*1728a

Overview

Group
SmallGroup(1728,30764)
Rank
5
Schläfli Type
{2,36,6,2}
Vertices, edges, …
2, 36, 108, 6, 2
Order of s0s1s2s3s4
36
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

12-fold

18-fold

27-fold

36-fold

54-fold

Covers minimal covers in bold

None in this atlas.

Representations

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