Polytope of Type {2,110}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,110}*440
if this polytope has a name.
Group : SmallGroup(440,50)
Rank : 3
Schlafli Type : {2,110}
Number of vertices, edges, etc : 2, 110, 110
Order of s₀s₁s₂ : 110
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,110,2} of size 880
   {2,110,4} of size 1760
Vertex Figure Of :
   {2,2,110} of size 880
   {3,2,110} of size 1320
   {4,2,110} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,55}*220
   5-fold quotients : {2,22}*88
   10-fold quotients : {2,11}*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 : {2,220}*880, {4,110}*880
   3-fold covers : {6,110}*1320, {2,330}*1320
   4-fold covers : {4,220}*1760, {2,440}*1760, {8,110}*1760
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope