Polytope of Type {6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 84, 336, 112
Order of s0s1s2 : 16
Order of s0s1s2s1 : 16
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*672c
   4-fold quotients : {6,4}*336
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)
(16,24)(17,21)(23,25)(26,29);;
s1 := ( 1, 3)( 2,28)( 4,21)( 5,27)( 6,31)( 7,17)( 8,22)( 9,13)(10,20)(11,25)
(12,30)(14,15)(16,23)(18,24)(19,26)(29,32);;
s2 := ( 1,32)( 2,30)( 3, 8)( 4,10)( 5,12)( 6, 7)( 9,25)(11,18)(13,22)(14,31)
(15,16)(17,26)(19,27)(20,24)(21,29)(23,28);;
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*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(32)!( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)
(15,20)(16,24)(17,21)(23,25)(26,29);
s1 := Sym(32)!( 1, 3)( 2,28)( 4,21)( 5,27)( 6,31)( 7,17)( 8,22)( 9,13)(10,20)
(11,25)(12,30)(14,15)(16,23)(18,24)(19,26)(29,32);
s2 := Sym(32)!( 1,32)( 2,30)( 3, 8)( 4,10)( 5,12)( 6, 7)( 9,25)(11,18)(13,22)
(14,31)(15,16)(17,26)(19,27)(20,24)(21,29)(23,28);
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*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope