Polytope of Type {22,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,10}*440
Also Known As : {22,10|2}. if this polytope has another name.
Group : SmallGroup(440,47)
Rank : 3
Schlafli Type : {22,10}
Number of vertices, edges, etc : 22, 110, 10
Order of s₀s₁s₂ : 110
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,10,2} of size 880
   {22,10,4} of size 1760
Vertex Figure Of :
   {2,22,10} of size 880
   {4,22,10} of size 1760
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {22,2}*88
   10-fold quotients : {11,2}*44
   11-fold quotients : {2,10}*40
   22-fold quotients : {2,5}*20
   55-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22,20}*880, {44,10}*880
   3-fold covers : {22,30}*1320, {66,10}*1320
   4-fold covers : {22,40}*1760, {88,10}*1760, {44,20}*1760
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);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 46)( 13, 45)( 14, 55)
( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)
( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)
( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)
( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)( 82, 97)
( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91);;
s2 := (  1, 67)(  2, 68)(  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)(  8, 74)
(  9, 75)( 10, 76)( 11, 77)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 60)
( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23,100)( 24,101)
( 25,102)( 26,103)( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)
( 33,110)( 34, 89)( 35, 90)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)
( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45, 78)( 46, 79)( 47, 80)( 48, 81)
( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88);;
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, 
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(110)!(  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);
s1 := Sym(110)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 46)( 13, 45)
( 14, 55)( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)
( 22, 47)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)
( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)
( 61, 63)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)
( 74,105)( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)
( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91);
s2 := Sym(110)!(  1, 67)(  2, 68)(  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)
(  8, 74)(  9, 75)( 10, 76)( 11, 77)( 12, 56)( 13, 57)( 14, 58)( 15, 59)
( 16, 60)( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23,100)
( 24,101)( 25,102)( 26,103)( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)
( 32,109)( 33,110)( 34, 89)( 35, 90)( 36, 91)( 37, 92)( 38, 93)( 39, 94)
( 40, 95)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45, 78)( 46, 79)( 47, 80)
( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88);
poly := sub<Sym(110)|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, 
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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