Polytope of Type {5,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6,6}*720a
if this polytope has a name.
Group : SmallGroup(720,767)
Rank : 4
Schlafli Type : {5,6,6}
Number of vertices, edges, etc : 10, 30, 36, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,6,6,2} of size 1440
Vertex Figure Of :
   {2,5,6,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,6,2}*240a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6,12}*1440a, {5,6,6}*1440a, {10,6,6}*1440a, {10,6,6}*1440b
Permutation Representation (GAP) :

s0 := (5,6)(7,8);;
s1 := (4,5)(6,7);;
s2 := (2,3)(7,8);;
s3 := (1,2);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(5,6)(7,8);
s1 := Sym(8)!(4,5)(6,7);
s2 := Sym(8)!(2,3)(7,8);
s3 := Sym(8)!(1,2);
poly := sub<Sym(8)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 >;

References : None.
to this polytope