Polytope of Type {7,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {7,6}
Number of vertices, edges, etc : 112, 336, 96
Order of s₀s₁s₂ : 28
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 : {7,6}*672b
   4-fold quotients : {7,6}*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 := ( 2, 4)( 3,21)( 6,30)( 7,13)( 8,20)( 9,24)(10,28)(11,19)(12,26)(15,29)
(16,32)(17,22)(23,31)(25,27);;
s2 := ( 1,11)( 2, 6)( 3,23)( 4,17)( 5,15)( 7,30)( 8,10)( 9,12)(13,28)(14,27)
(16,29)(18,32)(19,25)(20,22)(21,31)(24,26);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*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)!( 2, 4)( 3,21)( 6,30)( 7,13)( 8,20)( 9,24)(10,28)(11,19)(12,26)
(15,29)(16,32)(17,22)(23,31)(25,27);
s2 := Sym(32)!( 1,11)( 2, 6)( 3,23)( 4,17)( 5,15)( 7,30)( 8,10)( 9,12)(13,28)
(14,27)(16,29)(18,32)(19,25)(20,22)(21,31)(24,26);
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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1 >;

References : None.
to this polytope