Polytope of Type {5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5}*1920b
if this polytope has a name.
Group : SmallGroup(1920,241004)
Rank : 3
Schlafli Type : {5,5}
Number of vertices, edges, etc : 192, 480, 192
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5}*960
   32-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)
(21,28)(22,27)(23,32)(24,26);;
s1 := ( 2, 3)( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,21)(17,20)(18,22)(19,23)
(24,28)(25,26)(27,31)(29,30);;
s2 := ( 1,10)( 2, 6)( 3, 9)( 4,30)( 5, 7)( 8,15)(11,23)(13,25)(14,20)(16,32)
(18,22)(19,31)(21,28)(27,29);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)
(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 2, 3)( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,21)(17,20)(18,22)
(19,23)(24,28)(25,26)(27,31)(29,30);
s2 := Sym(32)!( 1,10)( 2, 6)( 3, 9)( 4,30)( 5, 7)( 8,15)(11,23)(13,25)(14,20)
(16,32)(18,22)(19,31)(21,28)(27,29);
poly := sub<Sym(32)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 >; 
 
References : None.
to this polytope