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}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240844)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 120, 480, 160
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,8}*960a, {6,4}*960, {6,8}*960b
   4-fold quotients : {6,8}*480a, {6,8}*480b, {6,4}*480
   8-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   16-fold quotients : {6,4}*120
   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=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 3.
      64 facets:
         48 of {6}*12
         16 of {2}*4
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 5.
      32 facets:
         32 of {6}*12
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 6.
      32 facets:
         24 of {6}*12
         8 of {2}*4
      20 vertex figures:
         20 of {8}*16

Permutation Representation (GAP) :

s0 := ( 1,38)( 2,33)( 3,21)( 4,36)( 5,19)( 6,34)( 7,17)( 8,22)( 9,32)(10,16)(11,30)(12,26)(13,20)(14,39)(15,37)(18,23)(24,40)(25,35)(29,31);;
s1 := ( 1, 4)( 2, 7)( 3,10)( 5,13)( 8,19)( 9,21)(11,25)(12,27)(14,29)(15,26)(16,32)(17,20)(18,22)(23,33)(28,37)(30,39)(31,38)(35,36)(42,44);;
s2 := ( 1,23)( 2,21)( 3,33)( 4,32)( 6,17)( 7,34)( 8,22)( 9,36)(11,15)(12,13)(18,38)(20,26)(24,35)(25,40)(27,28)(29,31)(30,37)(41,44)(42,43);;
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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(44)!( 1,38)( 2,33)( 3,21)( 4,36)( 5,19)( 6,34)( 7,17)( 8,22)( 9,32)(10,16)(11,30)(12,26)(13,20)(14,39)(15,37)(18,23)(24,40)(25,35)(29,31);
s1 := Sym(44)!( 1, 4)( 2, 7)( 3,10)( 5,13)( 8,19)( 9,21)(11,25)(12,27)(14,29)(15,26)(16,32)(17,20)(18,22)(23,33)(28,37)(30,39)(31,38)(35,36)(42,44);
s2 := Sym(44)!( 1,23)( 2,21)( 3,33)( 4,32)( 6,17)( 7,34)( 8,22)( 9,36)(11,15)(12,13)(18,38)(20,26)(24,35)(25,40)(27,28)(29,31)(30,37)(41,44)(42,43);
poly := sub<Sym(44)|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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0 >;

References : None.
to this polytope

Polytope of Type {6,8}

Twisty Puzzle