Polytope of Type {14,4}

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This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4}*784
Also Known As : {14,4}4. if this polytope has another name.
Group : SmallGroup(784,165)
Rank : 3
Schlafli Type : {14,4}
Number of vertices, edges, etc : 98, 196, 28
Order of s0s1s2 : 4
Order of s0s1s2s1 : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {14,4,2} of size 1568
Vertex Figure Of :
   {2,14,4} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {14,4}*392
   49-fold quotients : {2,4}*16
   98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,8}*1568a, {28,4}*1568
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 2.
      15 facets:
         13 of {14}*28
         2 of {7}*14
      49 vertex figures:
         49 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 7.
      4 facets:
         4 of {14}*28
      14 vertex figures:
         14 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 7.
      4 facets:
         4 of {14}*28
      14 vertex figures:
         14 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s2> of order 7.
      16 facets:
         2 of {14}*28
         14 of {2}*4
      14 vertex figures:
         14 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 14.
      9 facets:
         2 of {7}*14
         7 of {2}*4
      7 vertex figures:
         7 of {4}*8

Permutation Representation (GAP) : 
s0 := ( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,92)( 9,98)(10,97)(11,96)(12,95)(13,94)(14,93)(15,85)(16,91)(17,90)(18,89)(19,88)(20,87)(21,86)(22,78)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,64)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,57)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58);;
s1 := ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,36)(23,37)(24,38)(25,39)(26,40)(27,41)(28,42)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(64,92)(65,93)(66,94)(67,95)(68,96)(69,97)(70,98)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91);;
s2 := ( 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);;
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*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(98)!( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,92)( 9,98)(10,97)(11,96)(12,95)(13,94)(14,93)(15,85)(16,91)(17,90)(18,89)(19,88)(20,87)(21,86)(22,78)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,71)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,64)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,57)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58);
s1 := Sym(98)!( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,36)(23,37)(24,38)(25,39)(26,40)(27,41)(28,42)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63)(64,92)(65,93)(66,94)(67,95)(68,96)(69,97)(70,98)(71,85)(72,86)(73,87)(74,88)(75,89)(76,90)(77,91);
s2 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1 >;
References : None.
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