Polytope of Type {6,3} with group SmallGroup(144,183)

Overview

Group: SmallGroup(144,183)
Rank: 3
Schläfli Type: {6,3}
Vertices, edges, …: 24, 36, 12
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 6
Also known as: {6,3}_(2,2). if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{6,3}*48

4-fold

{6,3}*36

6-fold

{3,3}*24

12-fold

{2,3}*12

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

{6,15}*720e

6-fold

7-fold

{6,21}*1008b

8-fold

9-fold

10-fold

11-fold

{6,33}*1584

12-fold

13-fold

{6,39}*1872

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

6 facets

6 of {6}*12

12 vertex figures

12 of {3}*6

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

8 facets

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

12 vertex figures

12 of {3}*6

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

6 facets

3 of {2}*4
3 of {6}*12

8 vertex figures

8 of {3}*6

P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2> of order 4

3 facets

3 of {6}*12

6 vertex figures

6 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.