Polytope of Type {3,2,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,10}*720
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 5
Schlafli Type : {3,2,6,10}
Number of vertices, edges, etc : 3, 3, 6, 30, 10
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,6,10,2} of size 1440
Vertex Figure Of :
   {2,3,2,6,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,2,10}*240
   5-fold quotients : {3,2,6,2}*144
   6-fold quotients : {3,2,2,5}*120
   10-fold quotients : {3,2,3,2}*72
   15-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,12,10}*1440, {3,2,6,20}*1440a, {6,2,6,10}*1440
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)(10,11)(14,16)(15,17)(20,22)(21,23)(26,28)(27,29)(30,32)(31,33);;
s3 := ( 4, 6)( 5,10)( 8,15)( 9,14)(12,21)(13,20)(16,17)(18,27)(19,26)(22,23)
(24,31)(25,30)(28,29)(32,33);;
s4 := ( 4,12)( 5, 8)( 6,20)( 7,22)( 9,24)(10,14)(11,16)(13,18)(15,30)(17,32)
(19,25)(21,26)(23,28)(27,31)(29,33);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(33)!(2,3);
s1 := Sym(33)!(1,2);
s2 := Sym(33)!( 6, 7)(10,11)(14,16)(15,17)(20,22)(21,23)(26,28)(27,29)(30,32)
(31,33);
s3 := Sym(33)!( 4, 6)( 5,10)( 8,15)( 9,14)(12,21)(13,20)(16,17)(18,27)(19,26)
(22,23)(24,31)(25,30)(28,29)(32,33);
s4 := Sym(33)!( 4,12)( 5, 8)( 6,20)( 7,22)( 9,24)(10,14)(11,16)(13,18)(15,30)
(17,32)(19,25)(21,26)(23,28)(27,31)(29,33);
poly := sub<Sym(33)|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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope