Polytope of Type {6,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 90, 360, 120
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 : {6,4}*720
   3-fold quotients : {6,8}*480b
   6-fold quotients : {6,4}*240c
   12-fold quotients : {6,4}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      44 facets:
         38 of {6}*12
         6 of {2}*4
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 5.
      24 facets:
         24 of {6}*12
      18 vertex figures:
         18 of {8}*16

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle