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Polytope of Type {4,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,4}*720
if this polytope has a name.
Group : SmallGroup(720,763)
Rank : 4
Schlafli Type : {4,4,4}
Number of vertices, edges, etc : 10, 45, 45, 10
Order of s₀s₁s₂s₃ : 5
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Locally Toroidal
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,4,2} of size 1440
Vertex Figure Of :
   {2,4,4,4} of size 1440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4}*1440a, {4,4,4}*1440b, {4,4,4}*1440c, {4,4,4}*1440d, {4,4,4}*1440e
Permutation Representation (GAP) :

s0 := (4,6);;
s1 := (1,2)(3,4)(5,6);;
s2 := (2,3);;
s3 := (1,2)(3,5)(4,6);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s3*s0*s1*s2*s3*s2*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope