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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,8,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,8167)
Rank : 5
Schlafli Type : {5,2,8,10}
Number of vertices, edges, etc : 5, 5, 8, 40, 10
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 : {5,2,4,10}*800
   4-fold quotients : {5,2,2,10}*400
   5-fold quotients : {5,2,8,2}*320
   8-fold quotients : {5,2,2,5}*200
   10-fold quotients : {5,2,4,2}*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 := (16,21)(17,22)(18,23)(19,24)(20,25)(26,41)(27,42)(28,43)(29,44)(30,45)
(31,36)(32,37)(33,38)(34,39)(35,40);;
s3 := ( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,31)(12,35)(13,34)(14,33)(15,32)
(16,41)(17,45)(18,44)(19,43)(20,42)(21,36)(22,40)(23,39)(24,38)(25,37);;
s4 := ( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)(26,27)(28,30)
(31,32)(33,35)(36,37)(38,40)(41,42)(43,45);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(45)!(2,3)(4,5);
s1 := Sym(45)!(1,2)(3,4);
s2 := Sym(45)!(16,21)(17,22)(18,23)(19,24)(20,25)(26,41)(27,42)(28,43)(29,44)
(30,45)(31,36)(32,37)(33,38)(34,39)(35,40);
s3 := Sym(45)!( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,31)(12,35)(13,34)(14,33)
(15,32)(16,41)(17,45)(18,44)(19,43)(20,42)(21,36)(22,40)(23,39)(24,38)(25,37);
s4 := Sym(45)!( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)(26,27)
(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope