Polytope of Type {132,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {132,2}*528
if this polytope has a name.
Group : SmallGroup(528,148)
Rank : 3
Schlafli Type : {132,2}
Number of vertices, edges, etc : 132, 132, 2
Order of s0s1s2 : 132
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{132,2,2} of size 1056
{132,2,3} of size 1584
Vertex Figure Of :
{2,132,2} of size 1056
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {66,2}*264
3-fold quotients : {44,2}*176
4-fold quotients : {33,2}*132
6-fold quotients : {22,2}*88
11-fold quotients : {12,2}*48
12-fold quotients : {11,2}*44
22-fold quotients : {6,2}*24
33-fold quotients : {4,2}*16
44-fold quotients : {3,2}*12
66-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {132,4}*1056a, {264,2}*1056
3-fold covers : {396,2}*1584, {132,6}*1584b, {132,6}*1584c
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);;
s2 := (133,134);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(134)!( 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(134)!( 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);
s2 := Sym(134)!(133,134);
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*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope