Polytope of Type {10,3,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,3,2,3}*1800
if this polytope has a name.
Group : SmallGroup(1800,575)
Rank : 5
Schlafli Type : {10,3,2,3}
Number of vertices, edges, etc : 50, 75, 15, 3, 3
Order of s₀s₁s₂s₃s₄ : 6
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) :
   25-fold quotients : {2,3,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope