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Polytope of Type {3,2,4,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,14,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 6
Schlafli Type : {3,2,4,14,2}
Number of vertices, edges, etc : 3, 3, 4, 28, 14, 2
Order of s0s1s2s3s4s5 : 84
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,14,2}*672
4-fold quotients : {3,2,2,7,2}*336
7-fold quotients : {3,2,4,2,2}*192
14-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 9,14)(10,15)(16,22)(17,23)(24,28)(25,29);;
s3 := ( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,21)(15,20)(18,25)(19,24)
(22,27)(23,26)(28,31)(29,30);;
s4 := ( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(12,18)(13,20)(15,22)(17,24)(21,26)
(23,28)(27,30);;
s5 := (32,33);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(33)!(2,3);
s1 := Sym(33)!(1,2);
s2 := Sym(33)!( 5, 8)( 9,14)(10,15)(16,22)(17,23)(24,28)(25,29);
s3 := Sym(33)!( 4, 5)( 6,10)( 7, 9)( 8,13)(11,17)(12,16)(14,21)(15,20)(18,25)
(19,24)(22,27)(23,26)(28,31)(29,30);
s4 := Sym(33)!( 4, 6)( 5, 9)( 7,11)( 8,14)(10,16)(12,18)(13,20)(15,22)(17,24)
(21,26)(23,28)(27,30);
s5 := Sym(33)!(32,33);
poly := sub<Sym(33)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope