Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 112, 336, 84
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 16
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,6}*672c
   4-fold quotients : {4,6}*336
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 9)( 4, 5)( 6,31)( 7,21)( 8,19)(10,29)(11,26)(12,30)(13,14)
(15,28)(16,20)(17,27)(18,24)(22,25)(23,32);;
s1 := ( 1,11)( 2, 6)( 3,20)( 4,22)( 5,31)( 7,30)( 8,24)( 9,29)(10,13)(12,14)
(15,19)(16,27)(17,23)(18,32)(21,25)(26,28);;
s2 := ( 1, 3)( 2,10)( 4,19)( 5, 8)( 6,12)( 7,22)( 9,29)(11,27)(13,16)(14,20)
(15,32)(17,26)(18,24)(21,25)(23,28)(30,31);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 1, 3)( 2, 9)( 4, 5)( 6,31)( 7,21)( 8,19)(10,29)(11,26)(12,30)
(13,14)(15,28)(16,20)(17,27)(18,24)(22,25)(23,32);
s1 := Sym(32)!( 1,11)( 2, 6)( 3,20)( 4,22)( 5,31)( 7,30)( 8,24)( 9,29)(10,13)
(12,14)(15,19)(16,27)(17,23)(18,32)(21,25)(26,28);
s2 := Sym(32)!( 1, 3)( 2,10)( 4,19)( 5, 8)( 6,12)( 7,22)( 9,29)(11,27)(13,16)
(14,20)(15,32)(17,26)(18,24)(21,25)(23,28)(30,31);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope