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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,10,5}*1000
if this polytope has a name.
Group : SmallGroup(1000,183)
Rank : 5
Schlafli Type : {5,2,10,5}
Number of vertices, edges, etc : 5, 5, 10, 25, 5
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,10,5,2} of size 2000
Vertex Figure Of :
   {2,5,2,10,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,2,2,5}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,10,10}*2000b, {10,2,10,5}*2000
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);;
s3 := ( 6, 9)( 7,15)( 8,12)(10,17)(11,23)(13,25)(14,19)(16,21)(20,29)(22,26)
(24,27)(28,30);;
s4 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,20)(16,19)(17,22)(18,21)(23,24)(25,28)
(26,27)(29,30);;
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, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!(2,3)(4,5);
s1 := Sym(30)!(1,2)(3,4);
s2 := Sym(30)!( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30);
s3 := Sym(30)!( 6, 9)( 7,15)( 8,12)(10,17)(11,23)(13,25)(14,19)(16,21)(20,29)
(22,26)(24,27)(28,30);
s4 := Sym(30)!( 6, 7)( 8,11)( 9,13)(10,12)(15,20)(16,19)(17,22)(18,21)(23,24)
(25,28)(26,27)(29,30);
poly := sub<Sym(30)|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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope