Polytope of Type {4,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4}*784
Also Known As : {4,4}(7,7), {4,4}14. if this polytope has another name.
Group : SmallGroup(784,165)
Rank : 3
Schlafli Type : {4,4}
Number of vertices, edges, etc : 98, 196, 98
Order of s0s1s2 : 14
Order of s0s1s2s1 : 14
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
   Skewing Operation
Facet Of :
   {4,4,2} of size 1568
Vertex Figure Of :
   {2,4,4} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4}*392
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4}*1568
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<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> of order 2.
      49 facets:
         49 of {4}*8
      49 vertex figures:
         49 of {4}*8
   P/N, where N=<s0*s1*s0*s1> of order 2.
      50 facets:
         2 of {2}*4
         48 of {4}*8
      50 vertex figures:
         48 of {4}*8
         2 of {2}*4
   P/N, where N=<s0*s1*s0*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*s0*s1*s2> of order 4.
      25 facets:
         1 of {2}*4
         24 of {4}*8
      25 vertex figures:
         24 of {4}*8
         1 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 7.
      14 facets:
         14 of {4}*8
      14 vertex figures:
         14 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 7.
      14 facets:
         14 of {4}*8
      14 vertex figures:
         14 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2> of order 14.
      8 facets:
         2 of {2}*4
         6 of {4}*8
      8 vertex figures:
         6 of {4}*8
         2 of {2}*4
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 14.
      8 facets:
         2 of {2}*4
         6 of {4}*8
      8 vertex figures:
         6 of {4}*8
         2 of {2}*4

Permutation Representation (GAP) : 
s0 := ( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84);;
s1 := ( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)(42,48)(51,57)(52,64)(53,71)(54,78)(55,85)(56,92)(59,65)(60,72)(61,79)(62,86)(63,93)(67,73)(68,80)(69,87)(70,94)(75,81)(76,88)(77,95)(83,89)(84,96)(91,97);;
s2 := ( 1,51)( 2,50)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,58)( 9,57)(10,63)(11,62)(12,61)(13,60)(14,59)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)(21,66)(22,72)(23,71)(24,77)(25,76)(26,75)(27,74)(28,73)(29,79)(30,78)(31,84)(32,83)(33,82)(34,81)(35,80)(36,86)(37,85)(38,91)(39,90)(40,89)(41,88)(42,87)(43,93)(44,92)(45,98)(46,97)(47,96)(48,95)(49,94);;
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, 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(98)!( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(57,92)(58,93)(59,94)(60,95)(61,96)(62,97)(63,98)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84);
s1 := Sym(98)!( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)(42,48)(51,57)(52,64)(53,71)(54,78)(55,85)(56,92)(59,65)(60,72)(61,79)(62,86)(63,93)(67,73)(68,80)(69,87)(70,94)(75,81)(76,88)(77,95)(83,89)(84,96)(91,97);
s2 := Sym(98)!( 1,51)( 2,50)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,58)( 9,57)(10,63)(11,62)(12,61)(13,60)(14,59)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)(21,66)(22,72)(23,71)(24,77)(25,76)(26,75)(27,74)(28,73)(29,79)(30,78)(31,84)(32,83)(33,82)(34,81)(35,80)(36,86)(37,85)(38,91)(39,90)(40,89)(41,88)(42,87)(43,93)(44,92)(45,98)(46,97)(47,96)(48,95)(49,94);
poly := sub<Sym(98)|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, 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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