Polytope of Type {4,5,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240996)
Rank : 4
Schlafli Type : {4,5,4}
Number of vertices, edges, etc : 12, 120, 120, 16
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   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.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1> of order 2.
      8 facets:
         8 of {4,5}*120
      12 vertex figures:
         6 of 2-fold non-regular quotient of {5,4}*160
         6 of 2-fold non-regular quotient of {5,4}*160
   P/N, where N=<s1*s2*s3*s2*s1*s2*s3*s2*s3, s2*s1*s2*s3*s2*s1*s3*s2*s3> of order 4.
      4 facets:
         4 of {4,5}*120
      12 vertex figures:
         6 of 4-fold non-regular quotient of {5,4}*160
         6 of 4-fold non-regular quotient of {5,4}*160

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope