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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2,3}*864
if this polytope has a name.
Group : SmallGroup(864,4673)
Rank : 5
Schlafli Type : {3,6,2,3}
Number of vertices, edges, etc : 12, 36, 24, 3, 3
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,2,3,2} of size 1728
Vertex Figure Of :
   {2,3,6,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,6,2,3}*288
   4-fold quotients : {3,6,2,3}*216
   6-fold quotients : {3,3,2,3}*144
   12-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,2,3}*1728, {3,6,2,6}*1728, {6,6,2,3}*1728b
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11);;
s2 := ( 1, 2)( 5, 6)( 9,10);;
s3 := (14,15);;
s4 := (13,14);;
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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);
s1 := Sym(15)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11);
s2 := Sym(15)!( 1, 2)( 5, 6)( 9,10);
s3 := Sym(15)!(14,15);
s4 := Sym(15)!(13,14);
poly := sub<Sym(15)|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, s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

to this polytope