Polytope of Type {5,2,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,10,8}*1600
if this polytope has a name.
Group : SmallGroup(1600,8167)
Rank : 5
Schlafli Type : {5,2,10,8}
Number of vertices, edges, etc : 5, 5, 10, 40, 8
Order of s₀s₁s₂s₃s₄ : 40
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 : {5,2,10,4}*800
   4-fold quotients : {5,2,10,2}*400
   5-fold quotients : {5,2,2,8}*320
   8-fold quotients : {5,2,5,2}*200
   10-fold quotients : {5,2,2,4}*160
   20-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 := ( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)
(32,35)(33,34)(37,40)(38,39)(42,45)(43,44);;
s3 := ( 6, 7)( 8,10)(11,12)(13,15)(16,22)(17,21)(18,25)(19,24)(20,23)(26,42)
(27,41)(28,45)(29,44)(30,43)(31,37)(32,36)(33,40)(34,39)(35,38);;
s4 := ( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)
(16,41)(17,42)(18,43)(19,44)(20,45)(21,36)(22,37)(23,38)(24,39)(25,40);;
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*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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