Polytope of Type {12,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*960b
if this polytope has a name.
Group : SmallGroup(960,10882)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 120, 240, 40
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {12,4,2} of size 1920
Vertex Figure Of :
   {2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*480a, {12,4}*480b, {6,4}*480
   4-fold quotients : {6,4}*240a, {6,4}*240b, {6,4}*240c
   8-fold quotients : {6,4}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4}*1920a, {12,8}*1920a, {12,8}*1920b, {24,4}*1920c, {24,4}*1920d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      20 facets:
         20 of {12}*24
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      20 facets:
         20 of {12}*24
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      20 facets:
         20 of {12}*24
      64 vertex figures:
         56 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      20 facets:
         20 of {12}*24
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      16 facets:
         4 of {4}*8
         12 of {12}*24
      40 vertex figures:
         40 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      10 facets:
         10 of {12}*24
      32 vertex figures:
         28 of {4}*8
         4 of {2}*4
   P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      10 facets:
         10 of {12}*24
      32 vertex figures:
         28 of {4}*8
         4 of {2}*4
   P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      10 facets:
         10 of {12}*24
      32 vertex figures:
         28 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 6.
      8 facets:
         2 of {4}*8
         6 of {12}*24
      24 vertex figures:
         16 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 6.
      8 facets:
         2 of {4}*8
         6 of {12}*24
      20 vertex figures:
         20 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 6.
      8 facets:
         2 of {4}*8
         6 of {12}*24
      20 vertex figures:
         20 of {4}*8

Permutation Representation (GAP) :

s0 := (3,4)(7,8);;
s1 := (1,3)(2,4)(5,6)(8,9);;
s2 := ( 3, 4)( 6, 9)(10,11);;
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, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(3,4)(7,8);
s1 := Sym(11)!(1,3)(2,4)(5,6)(8,9);
s2 := Sym(11)!( 3, 4)( 6, 9)(10,11);
poly := sub<Sym(11)|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, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {12,4}

Twisty Puzzle