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}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240560)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 120, 480, 160
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*960
   4-fold quotients : {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   60-fold quotients : {2,8}*32
   120-fold quotients : {2,4}*16
   240-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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1> of order 3.
      64 facets:
         16 of {2}*4
         48 of {6}*12
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s1> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 5.
      32 facets:
         32 of {6}*12
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 6.
      32 facets:
         8 of {2}*4
         24 of {6}*12
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 6.
      32 facets:
         8 of {2}*4
         24 of {6}*12
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 6.
      32 facets:
         8 of {2}*4
         24 of {6}*12
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 10.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 10.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 10.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2> of order 12.
      24 facets:
         16 of {2}*4
         8 of {6}*12
      10 vertex figures:
         10 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s2*s1, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 20.
      8 facets:
         8 of {6}*12
      6 vertex figures:
         6 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s1, s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 20.
      8 facets:
         8 of {6}*12
      6 vertex figures:
         6 of {8}*16

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle