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

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

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

Permutation Representation (Magma) :

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

to this polytope