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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,3,3}*1920
Also Known As : hemi-5-cube, {4,3,3,3}₅. if this polytope has another name.
Group : SmallGroup(1920,240996)
Rank : 5
Schlafli Type : {4,3,3,3}
Number of vertices, edges, etc : 16, 40, 40, 20, 5
Order of s₀s₁s₂s₃s₄ : 5
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 4
Special Properties :
   Projective
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope