Polytope of Type {22,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,11}*484
if this polytope has a name.
Group : SmallGroup(484,9)
Rank : 3
Schlafli Type : {22,11}
Number of vertices, edges, etc : 22, 121, 11
Order of s₀s₁s₂ : 22
Order of s₀s₁s₂s₁ : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {22,11,2} of size 968
Vertex Figure Of :
   {2,22,11} of size 968
   {4,22,11} of size 1936
Quotients (Maximal Quotients in Boldface) :
   11-fold quotients : {2,11}*44
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22,22}*968b
   3-fold covers : {22,33}*1452
   4-fold covers : {22,44}*1936b, {44,22}*1936c
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);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12,112)( 13,111)( 14,121)
( 15,120)( 16,119)( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)
( 23,101)( 24,100)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)
( 31,104)( 32,103)( 33,102)( 34, 90)( 35, 89)( 36, 99)( 37, 98)( 38, 97)
( 39, 96)( 40, 95)( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 79)( 46, 78)
( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)
( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69);;
s2 := (  1, 12)(  2, 22)(  3, 21)(  4, 20)(  5, 19)(  6, 18)(  7, 17)(  8, 16)
(  9, 15)( 10, 14)( 11, 13)( 23,111)( 24,121)( 25,120)( 26,119)( 27,118)
( 28,117)( 29,116)( 30,115)( 31,114)( 32,113)( 33,112)( 34,100)( 35,110)
( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)( 41,104)( 42,103)( 43,102)
( 44,101)( 45, 89)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50, 95)( 51, 94)
( 52, 93)( 53, 92)( 54, 91)( 55, 90)( 56, 78)( 57, 88)( 58, 87)( 59, 86)
( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 79)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73);;
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, s2*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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