Polytope of Type {2,132}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,132}*528
if this polytope has a name.
Group : SmallGroup(528,148)
Rank : 3
Schlafli Type : {2,132}
Number of vertices, edges, etc : 2, 132, 132
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,132,2} of size 1056
Vertex Figure Of :
   {2,2,132} of size 1056
   {3,2,132} of size 1584
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,66}*264
   3-fold quotients : {2,44}*176
   4-fold quotients : {2,33}*132
   6-fold quotients : {2,22}*88
   11-fold quotients : {2,12}*48
   12-fold quotients : {2,11}*44
   22-fold quotients : {2,6}*24
   33-fold quotients : {2,4}*16
   44-fold quotients : {2,3}*12
   66-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,132}*1056a, {2,264}*1056
   3-fold covers : {2,396}*1584, {6,132}*1584b, {6,132}*1584c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14, 25)( 15, 35)( 16, 34)
( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 69,102)( 70,112)( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)( 76,106)
( 77,105)( 78,104)( 79,103)( 80,124)( 81,134)( 82,133)( 83,132)( 84,131)
( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,113)( 92,123)
( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)
(101,114);;
s2 := (  3, 81)(  4, 80)(  5, 90)(  6, 89)(  7, 88)(  8, 87)(  9, 86)( 10, 85)
( 11, 84)( 12, 83)( 13, 82)( 14, 70)( 15, 69)( 16, 79)( 17, 78)( 18, 77)
( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 92)( 26, 91)
( 27,101)( 28,100)( 29, 99)( 30, 98)( 31, 97)( 32, 96)( 33, 95)( 34, 94)
( 35, 93)( 36,114)( 37,113)( 38,123)( 39,122)( 40,121)( 41,120)( 42,119)
( 43,118)( 44,117)( 45,116)( 46,115)( 47,103)( 48,102)( 49,112)( 50,111)
( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)( 57,104)( 58,125)
( 59,124)( 60,134)( 61,133)( 62,132)( 63,131)( 64,130)( 65,129)( 66,128)
( 67,127)( 68,126);;
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*s1*s0*s1, s0*s2*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*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*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*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(134)!(1,2);
s1 := Sym(134)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14, 25)( 15, 35)
( 16, 34)( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)
( 24, 26)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)
( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)
( 57, 59)( 69,102)( 70,112)( 71,111)( 72,110)( 73,109)( 74,108)( 75,107)
( 76,106)( 77,105)( 78,104)( 79,103)( 80,124)( 81,134)( 82,133)( 83,132)
( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,113)
( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)
(100,115)(101,114);
s2 := Sym(134)!(  3, 81)(  4, 80)(  5, 90)(  6, 89)(  7, 88)(  8, 87)(  9, 86)
( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 70)( 15, 69)( 16, 79)( 17, 78)
( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 92)
( 26, 91)( 27,101)( 28,100)( 29, 99)( 30, 98)( 31, 97)( 32, 96)( 33, 95)
( 34, 94)( 35, 93)( 36,114)( 37,113)( 38,123)( 39,122)( 40,121)( 41,120)
( 42,119)( 43,118)( 44,117)( 45,116)( 46,115)( 47,103)( 48,102)( 49,112)
( 50,111)( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)( 57,104)
( 58,125)( 59,124)( 60,134)( 61,133)( 62,132)( 63,131)( 64,130)( 65,129)
( 66,128)( 67,127)( 68,126);
poly := sub<Sym(134)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*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*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*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*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 >;

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