Polytope of Type {4,2,2,2,2,3} with group SmallGroup(384,20133)

Overview

Group: SmallGroup(384,20133)
Rank: 7
Schläfli Type: {4,2,2,2,2,3}
Vertices, edges, …: 4, 4, 2, 2, 2, 3, 3
Order of s₀s₁s₂s₃s₄s₅s₆: 12
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

{4,2,2,2,2,3,2} ·768

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,2,2,2,2,3}*192

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

Permutation Representation (GAP)

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := ( 9,10);;
s5 := (12,13);;
s6 := (11,12);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s5*s6*s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!(5,6);
s3 := Sym(13)!(7,8);
s4 := Sym(13)!( 9,10);
s5 := Sym(13)!(12,13);
s6 := Sym(13)!(11,12);
poly := sub<Sym(13)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s5*s6*s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1 >;