Questions?
See the FAQ
or other info.

Polytope of Type {6,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,28}*1344d
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {6,28}
Number of vertices, edges, etc : 24, 336, 112
Order of s0s1s2 : 14
Order of s0s1s2s1 : 16
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {6,14}*672b
4-fold quotients : {6,7}*336
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 9)( 4, 5)( 6,31)( 7,21)( 8,19)(10,29)(11,26)(12,30)(13,14)
(15,28)(16,20)(17,27)(18,24)(22,25)(23,32);;
s1 := ( 2, 4)( 3,21)( 6,30)( 7,13)( 8,20)( 9,24)(10,28)(11,19)(12,26)(15,29)
(16,32)(17,22)(23,31)(25,27);;
s2 := ( 1, 6)( 2,17)( 3,31)( 4,14)( 5,13)( 7,28)( 8,19)( 9,27)(10,23)(11,25)
(12,24)(15,21)(16,20)(18,30)(22,26)(29,32);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

References : None.
to this polytope