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Polytope of Type {7,2,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,28}*784
if this polytope has a name.
Group : SmallGroup(784,125)
Rank : 4
Schlafli Type : {7,2,28}
Number of vertices, edges, etc : 7, 7, 28, 28
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{7,2,28,2} of size 1568
Vertex Figure Of :
{2,7,2,28} of size 1568
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {7,2,14}*392
4-fold quotients : {7,2,7}*196
7-fold quotients : {7,2,4}*112
14-fold quotients : {7,2,2}*56
Covers (Minimal Covers in Boldface) :
2-fold covers : {7,2,56}*1568, {14,2,28}*1568
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27)(28,29)
(30,33)(31,32)(34,35);;
s3 := ( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,28)(19,30)(21,24)(23,26)
(25,34)(27,31)(29,32)(33,35);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(35)!(2,3)(4,5)(6,7);
s1 := Sym(35)!(1,2)(3,4)(5,6);
s2 := Sym(35)!( 9,10)(11,12)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27)
(28,29)(30,33)(31,32)(34,35);
s3 := Sym(35)!( 8,14)( 9,11)(10,20)(12,22)(13,16)(15,18)(17,28)(19,30)(21,24)
(23,26)(25,34)(27,31)(29,32)(33,35);
poly := sub<Sym(35)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope