Polytope of Type {4,22,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,22,2,5}*1760
if this polytope has a name.
Group : SmallGroup(1760,1190)
Rank : 5
Schlafli Type : {4,22,2,5}
Number of vertices, edges, etc : 4, 44, 22, 5, 5
Order of s₀s₁s₂s₃s₄ : 220
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,22,2,5}*880
   4-fold quotients : {2,11,2,5}*440
   11-fold quotients : {4,2,2,5}*160
   22-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)
(33,44);;
s1 := ( 1,23)( 2,33)( 3,32)( 4,31)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)(10,25)
(11,24)(12,34)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)
(22,35);;
s2 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)
(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41);;
s3 := (46,47)(48,49);;
s4 := (45,46)(47,48);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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(49)!(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)
(32,43)(33,44);
s1 := Sym(49)!( 1,23)( 2,33)( 3,32)( 4,31)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)
(10,25)(11,24)(12,34)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)
(21,36)(22,35);
s2 := Sym(49)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)
(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41);
s3 := Sym(49)!(46,47)(48,49);
s4 := Sym(49)!(45,46)(47,48);
poly := sub<Sym(49)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

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