Polytope of Type {14,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,3}*588
Also Known As : {14,3}6. if this polytope has another name.
Group : SmallGroup(588,35)
Rank : 3
Schlafli Type : {14,3}
Number of vertices, edges, etc : 98, 147, 21
Order of s0s1s2 : 6
Order of s0s1s2s1 : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {14,3,2} of size 1176
Vertex Figure Of :
   {2,14,3} of size 1176
Quotients (Maximal Quotients in Boldface) :
   49-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,6}*1176a
   3-fold covers : {14,9}*1764, {42,3}*1764
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 7.
      3 facets:
         3 of {14}*28
      14 vertex figures:
         14 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 7.
      3 facets:
         3 of {14}*28
      14 vertex figures:
         14 of {3}*6
   P/N, where N=<s0*s1*s0*s1> of order 7.
      9 facets:
         7 of {2}*4
         2 of {14}*28
      14 vertex figures:
         14 of {3}*6

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