Polytope of Type {2,22,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,10}*880
if this polytope has a name.
Group : SmallGroup(880,217)
Rank : 4
Schlafli Type : {2,22,10}
Number of vertices, edges, etc : 2, 22, 110, 10
Order of s₀s₁s₂s₃ : 110
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,22,10,2} of size 1760
Vertex Figure Of :
   {2,2,22,10} of size 1760
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,22,2}*176
   10-fold quotients : {2,11,2}*88
   11-fold quotients : {2,2,10}*80
   22-fold quotients : {2,2,5}*40
   55-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,22,20}*1760, {2,44,10}*1760, {4,22,10}*1760
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)
( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)
( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)
( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)
(106,109)(107,108);;
s2 := (  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 48)( 15, 47)( 16, 57)
( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)
( 25, 37)( 26, 36)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)
( 69,103)( 70,102)( 71,112)( 72,111)( 73,110)( 74,109)( 75,108)( 76,107)
( 77,106)( 78,105)( 79,104)( 80, 92)( 81, 91)( 82,101)( 83,100)( 84, 99)
( 85, 98)( 86, 97)( 87, 96)( 88, 95)( 89, 94)( 90, 93);;
s3 := (  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)(  8, 74)(  9, 75)( 10, 76)
( 11, 77)( 12, 78)( 13, 79)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 62)
( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25,102)( 26,103)
( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34,111)
( 35,112)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)
( 43, 98)( 44, 99)( 45,100)( 46,101)( 47, 80)( 48, 81)( 49, 82)( 50, 83)
( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(112)!(1,2);
s1 := Sym(112)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)
( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)
(105,110)(106,109)(107,108);
s2 := Sym(112)!(  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 48)( 15, 47)
( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)
( 24, 49)( 25, 37)( 26, 36)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)
( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 58, 59)( 60, 68)( 61, 67)( 62, 66)
( 63, 65)( 69,103)( 70,102)( 71,112)( 72,111)( 73,110)( 74,109)( 75,108)
( 76,107)( 77,106)( 78,105)( 79,104)( 80, 92)( 81, 91)( 82,101)( 83,100)
( 84, 99)( 85, 98)( 86, 97)( 87, 96)( 88, 95)( 89, 94)( 90, 93);
s3 := Sym(112)!(  3, 69)(  4, 70)(  5, 71)(  6, 72)(  7, 73)(  8, 74)(  9, 75)
( 10, 76)( 11, 77)( 12, 78)( 13, 79)( 14, 58)( 15, 59)( 16, 60)( 17, 61)
( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25,102)
( 26,103)( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)
( 34,111)( 35,112)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)
( 42, 97)( 43, 98)( 44, 99)( 45,100)( 46,101)( 47, 80)( 48, 81)( 49, 82)
( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90);
poly := sub<Sym(112)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;

to this polytope