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}*1440b
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 120, 360, 90
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 12
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) :
   2-fold quotients : {4,6}*720
   3-fold quotients : {8,6}*480a
   6-fold quotients : {4,6}*240c
   12-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*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 3.
      30 facets:
         30 of {8}*16
      44 vertex figures:
         38 of {6}*12
         6 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 5.
      18 facets:
         18 of {8}*16
      24 vertex figures:
         24 of {6}*12

Permutation Representation (GAP) :

s0 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)(12,28)(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);;
s1 := ( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)(22,37)(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);;
s2 := ( 1, 2)( 5, 7)( 6, 8)( 9,32)(10,31)(11,30)(12,29)(13,14)(17,26)(18,27)(19,25)(20,28)(21,35)(22,34)(23,33)(24,36)(37,39)(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*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(43)!( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)(12,28)(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);
s1 := Sym(43)!( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)(22,37)(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);
s2 := Sym(43)!( 1, 2)( 5, 7)( 6, 8)( 9,32)(10,31)(11,30)(12,29)(13,14)(17,26)(18,27)(19,25)(20,28)(21,35)(22,34)(23,33)(24,36)(37,39)(41,42);
poly := sub<Sym(43)|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*s0*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2 >;

References : None.
to this polytope

Polytope of Type {8,6}

Twisty Puzzle