Polytope of Type {6,3,2} with group SmallGroup(288,1028)

Overview

Group: SmallGroup(288,1028)
Rank: 4
Schläfli Type: {6,3,2}
Vertices, edges, …: 24, 36, 12, 2
Order of s₀s₁s₂s₃: 12
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

{6,3,2}*96

4-fold

{6,3,2}*72

6-fold

{3,3,2}*48

12-fold

{2,3,2}*24

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

{6,15,2}*1440e

6-fold

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);;
s3 := (13,14);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(14)!( 3, 4)( 7, 8)(11,12);
s1 := Sym(14)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);
s2 := Sym(14)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,10);
s3 := Sym(14)!(13,14);
poly := sub<Sym(14)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;