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

Overview

Group: SmallGroup(1344,11291)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 84, 336, 112
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

{6,4}*672c

4-fold

{6,4}*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)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 7

16 facets

16 of {6}*12

12 vertex figures

12 of {8}*16

Representations

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

References

None.

to this polytope.