Polytope of Type {28,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6}*1680
if this polytope has a name.
Group : SmallGroup(1680,927)
Rank : 3
Schlafli Type : {28,6}
Number of vertices, edges, etc : 140, 420, 30
Order of s0s1s2 : 35
Order of s0s1s2s1 : 6
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) :
   7-fold quotients : {4,6}*240c
   14-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      15 facets:
         15 of {28}*56
      70 vertex figures:
         70 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         14 of {28}*56
         2 of {14}*28
      70 vertex figures:
         70 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      9 facets:
         3 of {14}*28
         6 of {28}*56
      35 vertex figures:
         35 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 2, 3)( 4, 5)( 6, 7)(10,12);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 9,10)(11,12);;
s2 := (8,9);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(12)!( 2, 3)( 4, 5)( 6, 7)(10,12);
s1 := Sym(12)!( 1, 2)( 3, 4)( 5, 6)( 9,10)(11,12);
s2 := Sym(12)!(8,9);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle