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}*960a
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 80, 240, 60
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 1920
Vertex Figure Of :
   {2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*480a, {8,6}*480b, {4,6}*480
   4-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   8-fold quotients : {4,6}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*1920a, {8,6}*1920b, {8,12}*1920d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 2.
      30 facets:
         30 of {8}*16
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 3.
      20 facets:
         20 of {8}*16
      32 vertex figures:
         24 of {6}*12
         8 of {2}*4
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      10 facets:
         10 of {8}*16
      16 vertex figures:
         12 of {6}*12
         4 of {2}*4

Permutation Representation (GAP) :

s0 := ( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);;
s1 := ( 3,11)( 4,12)( 5,14)( 6,13)( 7,40)( 8,39)( 9,41)(10,42)(15,34)(16,33)(17,32)(18,31)(19,25)(20,26)(21,23)(22,24)(27,28)(29,30);;
s2 := ( 1, 2)( 3,25)( 4,26)( 5,23)( 6,24)( 7,38)( 8,37)( 9,35)(10,36)(11,13)(12,14)(15,19)(16,20)(17,21)(18,22)(27,30)(28,29)(31,34)(32,33)(41,42);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(42)!( 5, 6)( 7,20)( 8,19)( 9,21)(10,22)(11,13)(12,14)(15,37)(16,38)(17,35)(18,36)(23,24)(27,32)(28,31)(29,34)(30,33)(39,40);
s1 := Sym(42)!( 3,11)( 4,12)( 5,14)( 6,13)( 7,40)( 8,39)( 9,41)(10,42)(15,34)(16,33)(17,32)(18,31)(19,25)(20,26)(21,23)(22,24)(27,28)(29,30);
s2 := Sym(42)!( 1, 2)( 3,25)( 4,26)( 5,23)( 6,24)( 7,38)( 8,37)( 9,35)(10,36)(11,13)(12,14)(15,19)(16,20)(17,21)(18,22)(27,30)(28,29)(31,34)(32,33)(41,42);
poly := sub<Sym(42)|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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {8,6}

Twisty Puzzle