Polytope of Type {8,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240558)
Rank : 3
Schlafli Type : {8,10}
Number of vertices, edges, etc : 96, 480, 120
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
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 : {8,10}*960a, {8,10}*960b, {4,10}*960
   4-fold quotients : {4,10}*480a, {4,10}*480b, {4,10}*480c
   8-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
   16-fold quotients : {4,5}*120
   60-fold quotients : {8,2}*32
   120-fold quotients : {4,2}*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*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      48 vertex figures:
         48 of {10}*20
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      48 vertex figures:
         48 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2> of order 2.
      60 facets:
         60 of {8}*16
      48 vertex figures:
         48 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 3.
      40 facets:
         40 of {8}*16
      32 vertex figures:
         32 of {10}*20
   P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2> of order 4.
      30 facets:
         30 of {8}*16
      24 vertex figures:
         24 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2> of order 4.
      30 facets:
         30 of {8}*16
      24 vertex figures:
         24 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 5.
      24 facets:
         24 of {8}*16
      32 vertex figures:
         16 of {10}*20
         16 of {2}*4
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 6.
      20 facets:
         20 of {8}*16
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2> of order 6.
      20 facets:
         20 of {8}*16
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 10.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         8 of {10}*20
         8 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 10.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         8 of {10}*20
         8 of {2}*4
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 12.
      10 facets:
         10 of {8}*16
      8 vertex figures:
         8 of {10}*20

Permutation Representation (GAP) :

s0 := ( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(18,21);;
s1 := ( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(18,19)(20,21);;
s2 := ( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(17,20)(18,21);;
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*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(18,21);
s1 := Sym(21)!( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(18,19)(20,21);
s2 := Sym(21)!( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(17,20)(18,21);
poly := sub<Sym(21)|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*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {8,10}

Twisty Puzzle