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Polytope of Type {7,14,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,14,2,2}*784
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 5
Schlafli Type : {7,14,2,2}
Number of vertices, edges, etc : 7, 49, 14, 2, 2
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{7,14,2,2,2} of size 1568
Vertex Figure Of :
{2,7,14,2,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
2-fold covers : {7,14,2,4}*1568, {7,14,4,2}*1568, {14,14,2,2}*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);;
s1 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,44)(16,43)(17,49)
(18,48)(19,47)(20,46)(21,45)(22,37)(23,36)(24,42)(25,41)(26,40)(27,39)(28,38)
(29,30)(31,35)(32,34);;
s2 := ( 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);;
s3 := (50,51);;
s4 := (52,53);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(53)!( 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(53)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,44)(16,43)
(17,49)(18,48)(19,47)(20,46)(21,45)(22,37)(23,36)(24,42)(25,41)(26,40)(27,39)
(28,38)(29,30)(31,35)(32,34);
s2 := Sym(53)!( 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);
s3 := Sym(53)!(50,51);
s4 := Sym(53)!(52,53);
poly := sub<Sym(53)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope