Polytope of Type {4,5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240995)
Rank : 4
Schlafli Type : {4,5,5}
Number of vertices, edges, etc : 32, 96, 120, 6
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) :
   16-fold quotients : {2,5,5}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)(18,19);;
s1 := ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)(16,20);;
s2 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,13)( 6,16)( 7,14)( 8,15)(17,18)(19,20);;
s3 := ( 1, 3)( 2, 4)( 5,17)( 6,20)( 7,18)( 8,19)( 9,15)(10,14)(11,13)(12,16);;
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*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s0*s2*s1*s0*s2*s1*s0*s1*s3*s2*s1*s2*s1*s3*s0*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)
(18,19);
s1 := Sym(20)!( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)
(16,20);
s2 := Sym(20)!( 1, 9)( 2,10)( 3,12)( 4,11)( 5,13)( 6,16)( 7,14)( 8,15)(17,18)
(19,20);
s3 := Sym(20)!( 1, 3)( 2, 4)( 5,17)( 6,20)( 7,18)( 8,19)( 9,15)(10,14)(11,13)
(12,16);
poly := sub<Sym(20)|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*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s0*s2*s1*s0*s2*s1*s0*s1*s3*s2*s1*s2*s1*s3*s0*s1*s2*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope