Polytope of Type {4,6,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,2,5}*960c
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 6
Schlafli Type : {4,6,2,2,5}
Number of vertices, edges, etc : 4, 12, 6, 2, 5, 5
Order of s₀s₁s₂s₃s₄s₅ : 30
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,2,5,2} of size 1920
Vertex Figure Of :
   {2,4,6,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3,2,2,5}*480
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2,2,5}*1920b, {4,12,2,2,5}*1920c, {4,6,4,2,5}*1920c, {4,6,2,2,5}*1920, {4,6,2,2,10}*1920c
Permutation Representation (GAP) :

s0 := (3,5)(4,6);;
s1 := (1,3)(2,5);;
s2 := (1,2)(3,4)(5,6);;
s3 := (7,8);;
s4 := (10,11)(12,13);;
s5 := ( 9,10)(11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(3,5)(4,6);
s1 := Sym(13)!(1,3)(2,5);
s2 := Sym(13)!(1,2)(3,4)(5,6);
s3 := Sym(13)!(7,8);
s4 := Sym(13)!(10,11)(12,13);
s5 := Sym(13)!( 9,10)(11,12);
poly := sub<Sym(13)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope