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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,22}*1760
if this polytope has a name.
Group : SmallGroup(1760,1190)
Rank : 5
Schlafli Type : {5,2,4,22}
Number of vertices, edges, etc : 5, 5, 4, 44, 22
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 : {5,2,2,22}*880
   4-fold quotients : {5,2,2,11}*440
   11-fold quotients : {5,2,4,2}*160
   22-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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