Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,124}

Atlas Canonical Name {6,124}*1488b

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Overview

Group
SmallGroup(1488,207)
Rank
3
Schläfli Type
{6,124}
Vertices, edges, …
6, 372, 124
Order of s0s1s2
93
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

31-fold

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

References

None.

to this polytope.

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