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Polytope of Type {14,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,14,2}*784c
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 4
Schlafli Type : {14,14,2}
Number of vertices, edges, etc : 14, 98, 14, 2
Order of s0s1s2s3 : 14
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,14,2,2} of size 1568
Vertex Figure Of :
   {2,14,14,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,14,2}*392
   7-fold quotients : {14,2,2}*112
   14-fold quotients : {7,2,2}*56
   49-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,14,2}*1568b, {14,14,4}*1568c, {14,28,2}*1568c
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)(51,56)(52,55)(53,54)(57,92)(58,98)(59,97)(60,96)(61,95)
(62,94)(63,93)(64,85)(65,91)(66,90)(67,89)(68,88)(69,87)(70,86)(71,78)(72,84)
(73,83)(74,82)(75,81)(76,80)(77,79);;
s1 := ( 1,58)( 2,57)( 3,63)( 4,62)( 5,61)( 6,60)( 7,59)( 8,51)( 9,50)(10,56)
(11,55)(12,54)(13,53)(14,52)(15,93)(16,92)(17,98)(18,97)(19,96)(20,95)(21,94)
(22,86)(23,85)(24,91)(25,90)(26,89)(27,88)(28,87)(29,79)(30,78)(31,84)(32,83)
(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73)(43,65)
(44,64)(45,70)(46,69)(47,68)(48,67)(49,66);;
s2 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)
(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)(46,47)
(51,56)(52,55)(53,54)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68)(72,77)(73,76)
(74,75)(79,84)(80,83)(81,82)(86,91)(87,90)(88,89)(93,98)(94,97)(95,96);;
s3 := ( 99,100);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(100)!( 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)(51,56)(52,55)(53,54)(57,92)(58,98)(59,97)(60,96)
(61,95)(62,94)(63,93)(64,85)(65,91)(66,90)(67,89)(68,88)(69,87)(70,86)(71,78)
(72,84)(73,83)(74,82)(75,81)(76,80)(77,79);
s1 := Sym(100)!( 1,58)( 2,57)( 3,63)( 4,62)( 5,61)( 6,60)( 7,59)( 8,51)( 9,50)
(10,56)(11,55)(12,54)(13,53)(14,52)(15,93)(16,92)(17,98)(18,97)(19,96)(20,95)
(21,94)(22,86)(23,85)(24,91)(25,90)(26,89)(27,88)(28,87)(29,79)(30,78)(31,84)
(32,83)(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73)
(43,65)(44,64)(45,70)(46,69)(47,68)(48,67)(49,66);
s2 := Sym(100)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)
(23,28)(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)
(46,47)(51,56)(52,55)(53,54)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68)(72,77)
(73,76)(74,75)(79,84)(80,83)(81,82)(86,91)(87,90)(88,89)(93,98)(94,97)(95,96);
s3 := Sym(100)!( 99,100);
poly := sub<Sym(100)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*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, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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