Polytope of Type {8,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*1344g
if this polytope has a name.
Group : SmallGroup(1344,11684)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 112, 336, 84
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 14
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 : {8,6}*672c, {8,6}*672d, {8,6}*672e
   4-fold quotients : {8,6}*336a
   168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 2.
      42 facets:
         42 of {8}*16
      56 vertex figures:
         56 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      42 facets:
         42 of {8}*16
      58 vertex figures:
         54 of {6}*12
         4 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 2.
      42 facets:
         42 of {8}*16
      56 vertex figures:
         56 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 7.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 14.
      6 facets:
         6 of {8}*16
      10 vertex figures:
         6 of {6}*12
         4 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 14.
      6 facets:
         6 of {8}*16
      8 vertex figures:
         8 of {6}*12

Permutation Representation (GAP) :

s0 := (3,8)(4,7)(5,6);;
s1 := ( 1, 3)( 2, 5)( 4, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 1, 2)( 4, 6)( 5, 7)( 9,11)(10,12);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(3,8)(4,7)(5,6);
s1 := Sym(12)!( 1, 3)( 2, 5)( 4, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(12)!( 1, 2)( 4, 6)( 5, 7)( 9,11)(10,12);
poly := sub<Sym(12)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {8,6}

Twisty Puzzle