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

Overview

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

{44,6}*528b

11-fold

{12,6}*144d

33-fold

{4,6}*48b

66-fold

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

Permutation Representation (Magma)

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

References