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Polytope of Type {28,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,7}*1344
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {28,7}
Number of vertices, edges, etc : 96, 336, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {14,7}*672
4-fold quotients : {7,7}*336
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)
(16,24)(17,21)(23,25)(26,29);;
s1 := ( 1, 3)( 2,32)( 4,22)( 5,26)( 6,12)( 7,11)( 8,21)( 9,20)(10,13)(14,23)
(15,16)(17,25)(18,24)(19,27)(28,29)(30,31);;
s2 := ( 1,11)( 2,30)( 3,15)( 4, 5)( 6, 7)( 8,16)( 9,26)(10,12)(13,14)(17,25)
(18,32)(19,20)(21,23)(22,31)(24,27)(28,29);;
poly := Group([s0,s1,s2]);;

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

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

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

References : None.
to this polytope