Polytope of Type {8,6} with group SmallGroup(1344,11291)

Overview

Group: SmallGroup(1344,11291)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 112, 336, 84
Order of s₀s₁s₂: 16
Order of s₀s₁s₂s₁: 16
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{4,6}*672c

4-fold

{4,6}*336

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^3*(s2*s1)^2*s0*s2*s1*s2> of order 7

12 facets

12 of {8}*16

16 vertex figures

16 of {6}*12

Representations

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

References

None.

to this polytope.