Polytope of Type {6,87} with group SmallGroup(1392,185)

Overview

Group: SmallGroup(1392,185)
Rank: 3
Schläfli Type: {6,87}
Vertices, edges, …: 8, 348, 116
Order of s₀s₁s₂: 116
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

12-fold

{2,29}*116

29-fold

{6,3}*48

58-fold

{3,3}*24

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

Permutation Representation (Magma)

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

References