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

Overview

Group: SmallGroup(192,1485)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 12, 48, 16
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
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{6,4}*96

4-fold

8-fold

16-fold

{3,2}*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*s2*s1)^3> of order 2

8 facets

8 of {6}*12

6 vertex figures

6 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.