Polytope of Type {6,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,44}*528a
Also Known As : {6,44|2}. if this polytope has another name.
Group : SmallGroup(528,108)
Rank : 3
Schlafli Type : {6,44}
Number of vertices, edges, etc : 6, 132, 44
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 :
   {6,44,2} of size 1056
Vertex Figure Of :
   {2,6,44} of size 1056
   {3,6,44} of size 1584
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,22}*264
   3-fold quotients : {2,44}*176
   6-fold quotients : {2,22}*88
   11-fold quotients : {6,4}*48a
   12-fold quotients : {2,11}*44
   22-fold quotients : {6,2}*24
   33-fold quotients : {2,4}*16
   44-fold quotients : {3,2}*12
   66-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,88}*1056, {12,44}*1056
   3-fold covers : {18,44}*1584a, {6,132}*1584a, {6,132}*1584b
Permutation Representation (GAP) :

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

References : None.
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