Polytope of Type {22,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,12}*528
Also Known As : {22,12|2}. if this polytope has another name.
Group : SmallGroup(528,107)
Rank : 3
Schlafli Type : {22,12}
Number of vertices, edges, etc : 22, 132, 12
Order of s₀s₁s₂ : 132
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,12,2} of size 1056
Vertex Figure Of :
   {2,22,12} of size 1056
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,6}*264
   3-fold quotients : {22,4}*176
   6-fold quotients : {22,2}*88
   11-fold quotients : {2,12}*48
   12-fold quotients : {11,2}*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 : {22,24}*1056, {44,12}*1056
   3-fold covers : {22,36}*1584, {66,12}*1584a, {66,12}*1584b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope