Polytope of Type {6,2,5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,5,10}*1200
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 5
Schlafli Type : {6,2,5,10}
Number of vertices, edges, etc : 6, 6, 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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,5,10}*600
   3-fold quotients : {2,2,5,10}*400
   5-fold quotients : {6,2,5,2}*240
   10-fold quotients : {3,2,5,2}*120
   15-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,24)(22,27)(23,26)
(28,31)(29,30);;
s3 := ( 7,13)( 8,10)( 9,20)(11,22)(12,16)(14,18)(15,24)(17,28)(19,23)(21,26)
(25,30)(27,29);;
s4 := (10,11)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);;
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*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(3,4)(5,6);
s1 := Sym(31)!(1,5)(2,3)(4,6);
s2 := Sym(31)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,24)(22,27)
(23,26)(28,31)(29,30);
s3 := Sym(31)!( 7,13)( 8,10)( 9,20)(11,22)(12,16)(14,18)(15,24)(17,28)(19,23)
(21,26)(25,30)(27,29);
s4 := Sym(31)!(10,11)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)
(30,31);
poly := sub<Sym(31)|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*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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