Polytope of Type {3,2,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,5}*600
if this polytope has a name.
Group : SmallGroup(600,174)
Rank : 5
Schlafli Type : {3,2,10,5}
Number of vertices, edges, etc : 3, 3, 10, 25, 5
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,10,5,2} of size 1200
Vertex Figure Of :
   {2,3,2,10,5} of size 1200
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {3,2,2,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,10,10}*1200b, {6,2,10,5}*1200
   3-fold covers : {9,2,10,5}*1800, {3,2,10,15}*1800, {3,6,10,5}*1800
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope