Polytope of Type {44,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,6}*528a
Also Known As : {44,6|2}. if this polytope has another name.
Group : SmallGroup(528,108)
Rank : 3
Schlafli Type : {44,6}
Number of vertices, edges, etc : 44, 132, 6
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 :
   {44,6,2} of size 1056
   {44,6,3} of size 1584
Vertex Figure Of :
   {2,44,6} of size 1056
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,6}*264
   3-fold quotients : {44,2}*176
   6-fold quotients : {22,2}*88
   11-fold quotients : {4,6}*48a
   12-fold quotients : {11,2}*44
   22-fold quotients : {2,6}*24
   33-fold quotients : {4,2}*16
   44-fold quotients : {2,3}*12
   66-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {88,6}*1056, {44,12}*1056
   3-fold covers : {44,18}*1584a, {132,6}*1584a, {132,6}*1584b
Irregular Quotients (of which this is a minimal cover):
   None.

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

Polytope of Type {44,6}

Twisty Puzzle