Polytope of Type {4,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5}*1200
if this polytope has a name.
Group : SmallGroup(1200,941)
Rank : 3
Schlafli Type : {4,5}
Number of vertices, edges, etc : 120, 300, 150
Order of s0s1s2 : 30
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {4,5}*240
   10-fold quotients : {4,5}*120
   60-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2.
      75 facets:
         75 of {4}*8
      60 vertex figures:
         60 of {5}*10
   P/N, where N=<s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2.
      80 facets:
         70 of {4}*8
         10 of {2}*4
      60 vertex figures:
         60 of {5}*10
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 3.
      50 facets:
         50 of {4}*8
      40 vertex figures:
         40 of {5}*10
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
      45 facets:
         15 of {2}*4
         30 of {4}*8
      30 vertex figures:
         30 of {5}*10
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      40 facets:
         35 of {4}*8
         5 of {2}*4
      30 vertex figures:
         30 of {5}*10
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 5.
      30 facets:
         30 of {4}*8
      24 vertex figures:
         24 of {5}*10
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 6.
      30 facets:
         20 of {4}*8
         10 of {2}*4
      20 vertex figures:
         20 of {5}*10
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 10.
      20 facets:
         10 of {4}*8
         10 of {2}*4
      12 vertex figures:
         12 of {5}*10
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 12.
      15 facets:
         5 of {2}*4
         10 of {4}*8
      10 vertex figures:
         10 of {5}*10
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 20.
      10 facets:
         5 of {4}*8
         5 of {2}*4
      6 vertex figures:
         6 of {5}*10

Permutation Representation (GAP) : 
s0 := (3,4);;
s1 := ( 2, 3)( 4, 5)( 7, 8)( 9,10);;
s2 := (1,2)(3,4)(6,7)(8,9);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(10)!(3,4);
s1 := Sym(10)!( 2, 3)( 4, 5)( 7, 8)( 9,10);
s2 := Sym(10)!(1,2)(3,4)(6,7)(8,9);
poly := sub<Sym(10)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle