Polytope of Type {2,3,6} with group SmallGroup(72,46)

Overview

Group: SmallGroup(72,46)
Rank: 4
Schläfli Type: {2,3,6}
Vertices, edges, …: 2, 3, 9, 6
Order of s₀s₁s₂s₃: 6
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{2,3,2}*24

Covers minimal covers in bold

2-fold

{2,6,6}*144c

3-fold

4-fold

5-fold

{2,15,6}*360

6-fold

7-fold

{2,21,6}*504

8-fold

9-fold

10-fold

11-fold

{2,33,6}*792

12-fold

13-fold

{2,39,6}*936

14-fold

15-fold

16-fold

17-fold

{2,51,6}*1224

18-fold

19-fold

{2,57,6}*1368

20-fold

21-fold

22-fold

23-fold

{2,69,6}*1656

24-fold

25-fold

26-fold

27-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,10);;
s2 := ( 3, 8)( 4, 6)( 5,10)( 7, 9);;
s3 := ( 6, 7)( 8, 9)(10,11);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(11)!(1,2);
s1 := Sym(11)!( 4, 5)( 6, 7)( 8,11)( 9,10);
s2 := Sym(11)!( 3, 8)( 4, 6)( 5,10)( 7, 9);
s3 := Sym(11)!( 6, 7)( 8, 9)(10,11);
poly := sub<Sym(11)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;