Polytope of Type {2,5,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,2,40}*1600
if this polytope has a name.
Group : SmallGroup(1600,8115)
Rank : 5
Schlafli Type : {2,5,2,40}
Number of vertices, edges, etc : 2, 5, 5, 40, 40
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 : {2,5,2,20}*800
   4-fold quotients : {2,5,2,10}*400
   5-fold quotients : {2,5,2,8}*320
   8-fold quotients : {2,5,2,5}*200
   10-fold quotients : {2,5,2,4}*160
   20-fold quotients : {2,5,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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