Polytope of Type {6,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*432
Also Known As : {6,3}(6,0), {6,3}12. if this polytope has another name.
Group : SmallGroup(432,523)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 72, 108, 36
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,3,2} of size 864
   {6,3,4} of size 1728
Vertex Figure Of :
   {2,6,3} of size 864
   {4,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,3}*144
   4-fold quotients : {6,3}*108
   9-fold quotients : {6,3}*48
   12-fold quotients : {6,3}*36
   18-fold quotients : {3,3}*24
   36-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,3}*864, {6,6}*864b
   3-fold covers : {6,9}*1296a, {6,3}*1296, {6,9}*1296b, {18,3}*1296a, {6,9}*1296c, {6,9}*1296d
   4-fold covers : {6,3}*1728, {6,12}*1728a, {12,6}*1728c, {6,6}*1728a, {6,12}*1728d, {12,6}*1728e, {12,3}*1728
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 2.
      18 facets:
         18 of {6}*12
      36 vertex figures:
         36 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 2.
      20 facets:
         4 of {3}*6
         16 of {6}*12
      36 vertex figures:
         36 of {3}*6
   P/N, where N=<s0*s1*s0*s1> of order 3.
      14 facets:
         3 of {2}*4
         11 of {6}*12
      24 vertex figures:
         24 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 3.
      12 facets:
         12 of {6}*12
      24 vertex figures:
         24 of {3}*6
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
      9 facets:
         9 of {6}*12
      18 vertex figures:
         18 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      9 facets:
         9 of {6}*12
      18 vertex figures:
         18 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 6.
      6 facets:
         6 of {6}*12
      12 vertex figures:
         12 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s0*s1*s2> of order 6.
      8 facets:
         4 of {3}*6
         4 of {6}*12
      12 vertex figures:
         12 of {3}*6

Permutation Representation (GAP) : 
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);;
s1 := ( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31);;
s2 := ( 1,16)( 2,14)( 3,15)( 4,13)( 5,20)( 6,18)( 7,19)( 8,17)( 9,24)(10,22)(11,23)(12,21)(25,28)(29,32)(33,36);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(36)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);
s1 := Sym(36)!( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31);
s2 := Sym(36)!( 1,16)( 2,14)( 3,15)( 4,13)( 5,20)( 6,18)( 7,19)( 8,17)( 9,24)(10,22)(11,23)(12,21)(25,28)(29,32)(33,36);
poly := sub<Sym(36)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle