Polytope of Type {8,6} with group SmallGroup(192,1485)

Overview

Group: SmallGroup(192,1485)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 16, 48, 12
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{4,6}*96

4-fold

8-fold

16-fold

{2,3}*12

24-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

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*s0*s2)^2*s1*s2> of order 2

6 facets

6 of {8}*16

8 vertex figures

8 of {6}*12

Representations

Permutation Representation (GAP)

s0 := ( 1,11)( 2,12)( 3,10)( 4, 9)( 5,15)( 6,16)( 7,14)( 8,13);;
s1 := ( 3, 5)( 4, 6)( 7, 8)(11,13)(12,14)(15,16);;
s2 := ( 3, 4)( 5, 7)( 6, 8)( 9,10)(13,16)(14,15);;
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*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(16)!( 1,11)( 2,12)( 3,10)( 4, 9)( 5,15)( 6,16)( 7,14)( 8,13);
s1 := Sym(16)!( 3, 5)( 4, 6)( 7, 8)(11,13)(12,14)(15,16);
s2 := Sym(16)!( 3, 4)( 5, 7)( 6, 8)( 9,10)(13,16)(14,15);
poly := sub<Sym(16)|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*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.