Polytope of Type {3,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6}*588
Also Known As : {3,6}(7,0), {3,6}14. if this polytope has another name.
Group : SmallGroup(588,35)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 49, 147, 98
Order of s0s1s2 : 14
Order of s0s1s2s1 : 6
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,6,2} of size 1176
Vertex Figure Of :
   {2,3,6} of size 1176
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*1176b
   3-fold covers : {3,6}*1764
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 7.
      14 facets:
         14 of {3}*6
      7 vertex figures:
         7 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 7.
      14 facets:
         14 of {3}*6
      7 vertex figures:
         7 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 2,22)( 3,43)( 4,15)( 5,36)( 6, 8)( 7,29)( 9,27)(10,48)(11,20)(12,41)(14,34)(16,25)(17,46)(19,39)(21,32)(24,44)(26,37)(28,30)(31,49)(33,42)(38,47);;
s1 := ( 2,43)( 3,36)( 4,29)( 5,22)( 6,15)( 7, 8)( 9,49)(10,42)(11,35)(12,28)(13,21)(16,48)(17,41)(18,34)(19,27)(23,47)(24,40)(25,33)(30,46)(31,39)(37,45);;
s2 := ( 1,23)( 3,30)( 4, 9)( 5,37)( 6,16)( 7,44)( 8,25)(10,32)(12,39)(13,18)(14,46)(15,27)(17,34)(19,41)(21,48)(24,29)(26,36)(28,43)(33,38)(35,45)(42,47);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(49)!( 2,22)( 3,43)( 4,15)( 5,36)( 6, 8)( 7,29)( 9,27)(10,48)(11,20)(12,41)(14,34)(16,25)(17,46)(19,39)(21,32)(24,44)(26,37)(28,30)(31,49)(33,42)(38,47);
s1 := Sym(49)!( 2,43)( 3,36)( 4,29)( 5,22)( 6,15)( 7, 8)( 9,49)(10,42)(11,35)(12,28)(13,21)(16,48)(17,41)(18,34)(19,27)(23,47)(24,40)(25,33)(30,46)(31,39)(37,45);
s2 := Sym(49)!( 1,23)( 3,30)( 4, 9)( 5,37)( 6,16)( 7,44)( 8,25)(10,32)(12,39)(13,18)(14,46)(15,27)(17,34)(19,41)(21,48)(24,29)(26,36)(28,43)(33,38)(35,45)(42,47);
poly := sub<Sym(49)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
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