Polytope of Type {5,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,2}*1000
if this polytope has a name.
Group : SmallGroup(1000,106)
Rank : 4
Schlafli Type : {5,10,2}
Number of vertices, edges, etc : 25, 125, 50, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,10,2,2} of size 2000
Vertex Figure Of :
   {2,5,10,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {5,10,2}*200
   25-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,10,4}*2000a, {10,10,2}*2000a
Permutation Representation (GAP) :

s0 := ( 6,21)( 7,22)( 8,23)( 9,24)(10,25)(11,16)(12,17)(13,18)(14,19)(15,20);;
s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5, 6)(11,23)(12,24)(13,25)(14,21)(15,22);;
s2 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17);;
s3 := (26,27);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1 >;

to this polytope