Polytope of Type {6,6} with group SmallGroup(192,955)

Overview

Group: SmallGroup(192,955)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 16, 48, 16
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 3
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Related Polytopes

Constructions

Facet of

{6,6,2} ·384

Vertex figure of

{2,6,6} ·384

Quotients maximal quotients in bold

8-fold

{3,3}*24

Covers minimal covers in bold

2-fold

4-fold

6-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)^3> of order 2

10 facets

4 of {3}*6
6 of {6}*12

10 vertex figures

6 of {6}*12
4 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.