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Polytope of Type {28,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,6,2,2}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {28,6,2,2}
Number of vertices, edges, etc : 28, 84, 6, 2, 2
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
7-fold quotients : {4,6,2,2}*192b
14-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,23)(10,24)(11,21)(12,22)
(13,19)(14,20)(15,17)(16,18);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,25)(10,27)(11,26)(12,28)(13,21)(14,23)
(15,22)(16,24)(18,19);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28);;
s3 := (29,30);;
s4 := (31,32);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0 ];;
poly := F / rels;;

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

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