Polytope of Type {3,4,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,4,3}*576
Also Known As : {{3,4}₃,{4,4}₄,{4,3}₃}. if this polytope has another name.
Group : SmallGroup(576,8654)
Rank : 5
Schlafli Type : {3,4,4,3}
Number of vertices, edges, etc : 3, 12, 16, 12, 3
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 4
Special Properties :
   Universal
   Non-Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,4,3,2} of size 1152
Vertex Figure Of :
   {2,3,4,4,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,4,6}*1152c, {6,4,4,3}*1152c
   3-fold covers : {3,4,4,9}*1728, {9,4,4,3}*1728
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope