Polytope of Type {6,132} with group SmallGroup(1584,663)

Overview

Group: SmallGroup(1584,663)
Rank: 3
Schläfli Type: {6,132}
Vertices, edges, …: 6, 396, 132
Order of s₀s₁s₂: 33
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

3-fold

{6,44}*528b

11-fold

{6,12}*144d

33-fold

{6,4}*48b

66-fold

{3,4}*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)(119,120)(123,124)(127,128)(131,132);;
s1 := (  2,  4)(  5, 41)(  6, 44)(  7, 43)(  8, 42)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 21, 25)( 22, 28)( 23, 27)( 24, 26)( 45, 89)( 46, 92)( 47, 91)( 48, 90)( 49,129)( 50,132)( 51,131)( 52,130)( 53,125)( 54,128)( 55,127)( 56,126)( 57,121)( 58,124)( 59,123)( 60,122)( 61,117)( 62,120)( 63,119)( 64,118)( 65,113)( 66,116)( 67,115)( 68,114)( 69,109)( 70,112)( 71,111)( 72,110)( 73,105)( 74,108)( 75,107)( 76,106)( 77,101)( 78,104)( 79,103)( 80,102)( 81, 97)( 82,100)( 83, 99)( 84, 98)( 85, 93)( 86, 96)( 87, 95)( 88, 94);;
s2 := (  1, 50)(  2, 49)(  3, 52)(  4, 51)(  5, 46)(  6, 45)(  7, 48)(  8, 47)(  9, 86)( 10, 85)( 11, 88)( 12, 87)( 13, 82)( 14, 81)( 15, 84)( 16, 83)( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 74)( 22, 73)( 23, 76)( 24, 75)( 25, 70)( 26, 69)( 27, 72)( 28, 71)( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 62)( 34, 61)( 35, 64)( 36, 63)( 37, 58)( 38, 57)( 39, 60)( 40, 59)( 41, 54)( 42, 53)( 43, 56)( 44, 55)( 89, 94)( 90, 93)( 91, 96)( 92, 95)( 97,130)( 98,129)( 99,132)(100,131)(101,126)(102,125)(103,128)(104,127)(105,122)(106,121)(107,124)(108,123)(109,118)(110,117)(111,120)(112,119)(113,114)(115,116);;
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, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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*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(132)!(  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)(127,128)(131,132);
s1 := Sym(132)!(  2,  4)(  5, 41)(  6, 44)(  7, 43)(  8, 42)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 21, 25)( 22, 28)( 23, 27)( 24, 26)( 45, 89)( 46, 92)( 47, 91)( 48, 90)( 49,129)( 50,132)( 51,131)( 52,130)( 53,125)( 54,128)( 55,127)( 56,126)( 57,121)( 58,124)( 59,123)( 60,122)( 61,117)( 62,120)( 63,119)( 64,118)( 65,113)( 66,116)( 67,115)( 68,114)( 69,109)( 70,112)( 71,111)( 72,110)( 73,105)( 74,108)( 75,107)( 76,106)( 77,101)( 78,104)( 79,103)( 80,102)( 81, 97)( 82,100)( 83, 99)( 84, 98)( 85, 93)( 86, 96)( 87, 95)( 88, 94);
s2 := Sym(132)!(  1, 50)(  2, 49)(  3, 52)(  4, 51)(  5, 46)(  6, 45)(  7, 48)(  8, 47)(  9, 86)( 10, 85)( 11, 88)( 12, 87)( 13, 82)( 14, 81)( 15, 84)( 16, 83)( 17, 78)( 18, 77)( 19, 80)( 20, 79)( 21, 74)( 22, 73)( 23, 76)( 24, 75)( 25, 70)( 26, 69)( 27, 72)( 28, 71)( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 62)( 34, 61)( 35, 64)( 36, 63)( 37, 58)( 38, 57)( 39, 60)( 40, 59)( 41, 54)( 42, 53)( 43, 56)( 44, 55)( 89, 94)( 90, 93)( 91, 96)( 92, 95)( 97,130)( 98,129)( 99,132)(100,131)(101,126)(102,125)(103,128)(104,127)(105,122)(106,121)(107,124)(108,123)(109,118)(110,117)(111,120)(112,119)(113,114)(115,116);
poly := sub<Sym(132)|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, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References