Questions?
See the FAQ
or other info.

Polytope of Type {3,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,16}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {3,16}
Number of vertices, edges, etc : 42, 336, 224
Order of s0s1s2 : 16
Order of s0s1s2s1 : 16
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {3,8}*672b
4-fold quotients : {3,8}*336b
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 := ( 1, 3)( 2,14)( 4,17)( 5, 7)( 6,31)( 8,11)( 9,15)(10,23)(12,30)(13,28)
(16,29)(18,24)(19,25)(20,32)(21,27)(22,26);;
s2 := ( 1, 4)( 2, 7)( 3, 5)( 6,16)( 8,12)( 9,21)(10,17)(13,18)(14,24)(15,25)
(19,30)(20,31)(22,28)(27,29);;
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, s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
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)!( 1, 3)( 2,14)( 4,17)( 5, 7)( 6,31)( 8,11)( 9,15)(10,23)(12,30)
(13,28)(16,29)(18,24)(19,25)(20,32)(21,27)(22,26);
s2 := Sym(32)!( 1, 4)( 2, 7)( 3, 5)( 6,16)( 8,12)( 9,21)(10,17)(13,18)(14,24)
(15,25)(19,30)(20,31)(22,28)(27,29);
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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope