Polytope of Type {22,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,3}*1452
Also Known As : {22,3}6. if this polytope has another name.
Group : SmallGroup(1452,22)
Rank : 3
Schlafli Type : {22,3}
Number of vertices, edges, etc : 242, 363, 33
Order of s0s1s2 : 6
Order of s0s1s2s1 : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   121-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 11.
      3 facets:
         3 of {22}*44
      22 vertex figures:
         22 of {3}*6
   P/N, where N=<s0*s1*s0*s1> of order 11.
      13 facets:
         11 of {2}*4
         2 of {22}*44
      22 vertex figures:
         22 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 11.
      3 facets:
         3 of {22}*44
      22 vertex figures:
         22 of {3}*6

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