Polytope of Type {8,14}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14}*1568b
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 3
Schlafli Type : {8,14}
Number of vertices, edges, etc : 56, 392, 98
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,14}*784a
   49-fold quotients : {8,2}*32
   98-fold quotients : {4,2}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 7.
      14 facets:
         14 of {8}*16
      20 vertex figures:
         6 of {14}*28
         14 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 7.
      14 facets:
         14 of {8}*16
      8 vertex figures:
         8 of {14}*28

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,14}

Twisty Puzzle