Polytope of Type {10,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,22}*440
Also Known As : {10,22|2}. if this polytope has another name.
Group : SmallGroup(440,47)
Rank : 3
Schlafli Type : {10,22}
Number of vertices, edges, etc : 10, 110, 22
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 :
   {10,22,2} of size 880
   {10,22,4} of size 1760
Vertex Figure Of :
   {2,10,22} of size 880
   {4,10,22} of size 1760
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,22}*88
   10-fold quotients : {2,11}*44
   11-fold quotients : {10,2}*40
   22-fold quotients : {5,2}*20
   55-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,22}*880, {10,44}*880
   3-fold covers : {30,22}*1320, {10,66}*1320
   4-fold covers : {40,22}*1760, {10,88}*1760, {20,44}*1760
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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