Polytope of Type {3,2,6,3} with group SmallGroup(216,162)

Overview

Group: SmallGroup(216,162)
Rank: 5
Schläfli Type: {3,2,6,3}
Vertices, edges, …: 3, 3, 6, 9, 3
Order of s₀s₁s₂s₃s₄: 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 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

{3,2,2,3}*72

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

Representations

Permutation Representation (GAP)

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7, 8)( 9,10)(11,12);;
s3 := ( 4, 7)( 5,11)( 6, 9)(10,12);;
s4 := ( 4, 5)( 7,10)( 8, 9)(11,12);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2);
s2 := Sym(12)!( 7, 8)( 9,10)(11,12);
s3 := Sym(12)!( 4, 7)( 5,11)( 6, 9)(10,12);
s4 := Sym(12)!( 4, 5)( 7,10)( 8, 9)(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 >;