Questions?
See the FAQ
or other info.

Polytope of Type {132}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {132}*264
Also Known As : 132-gon, {132}. if this polytope has another name.
Group : SmallGroup(264,25)
Rank : 2
Schlafli Type : {132}
Number of vertices, edges, etc : 132, 132
Order of s0s1 : 132
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {132,2} of size 528
   {132,4} of size 1056
   {132,4} of size 1056
   {132,4} of size 1056
   {132,6} of size 1584
   {132,6} of size 1584
   {132,6} of size 1584
   {132,6} of size 1584
Vertex Figure Of :
   {2,132} of size 528
   {4,132} of size 1056
   {4,132} of size 1056
   {4,132} of size 1056
   {6,132} of size 1584
   {6,132} of size 1584
   {6,132} of size 1584
   {6,132} of size 1584
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {66}*132
   3-fold quotients : {44}*88
   4-fold quotients : {33}*66
   6-fold quotients : {22}*44
   11-fold quotients : {12}*24
   12-fold quotients : {11}*22
   22-fold quotients : {6}*12
   33-fold quotients : {4}*8
   44-fold quotients : {3}*6
   66-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {264}*528
   3-fold covers : {396}*792
   4-fold covers : {528}*1056
   5-fold covers : {660}*1320
   6-fold covers : {792}*1584
   7-fold covers : {924}*1848
Permutation Representation (GAP) :
s0 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 23)( 13, 33)( 14, 32)
( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)
( 75,103)( 76,102)( 77,101)( 78,122)( 79,132)( 80,131)( 81,130)( 82,129)
( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)( 89,111)( 90,121)
( 91,120)( 92,119)( 93,118)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)
( 99,112);;
s1 := (  1, 79)(  2, 78)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 83)
(  9, 82)( 10, 81)( 11, 80)( 12, 68)( 13, 67)( 14, 77)( 15, 76)( 16, 75)
( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 90)( 24, 89)
( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)( 32, 92)
( 33, 91)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,101)( 46,100)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)( 56,123)
( 57,122)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)
( 65,125)( 66,124);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(132)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 23)( 13, 33)
( 14, 32)( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)
( 22, 24)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)
( 55, 57)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)
( 74,104)( 75,103)( 76,102)( 77,101)( 78,122)( 79,132)( 80,131)( 81,130)
( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)( 89,111)
( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)( 95,116)( 96,115)( 97,114)
( 98,113)( 99,112);
s1 := Sym(132)!(  1, 79)(  2, 78)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)
(  8, 83)(  9, 82)( 10, 81)( 11, 80)( 12, 68)( 13, 67)( 14, 77)( 15, 76)
( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 90)
( 24, 89)( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)
( 32, 92)( 33, 91)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,101)( 46,100)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)
( 56,123)( 57,122)( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)
( 64,126)( 65,125)( 66,124);
poly := sub<Sym(132)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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 >; 
 
References : None.
to this polytope