Polytope of Type {6,6,2} with group SmallGroup(144,192)

Overview

Group: SmallGroup(144,192)
Rank: 4
Schläfli Type: {6,6,2}
Vertices, edges, …: 6, 18, 6, 2
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

2-fold

{3,6,2}*72

3-fold

{6,2,2}*48

6-fold

{3,2,2}*24

9-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,18)(16,17);;
s1 := ( 1,15)( 2,11)( 3, 9)( 4,17)( 5, 7)( 6,16)( 8,13)(10,12)(14,18);;
s2 := ( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := (19,20);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(20)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,18)(16,17);
s1 := Sym(20)!( 1,15)( 2,11)( 3, 9)( 4,17)( 5, 7)( 6,16)( 8,13)(10,12)(14,18);
s2 := Sym(20)!( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 >;