Polytope of Type {8,4,2}

Atlas Canonical Name {8,4,2}*1344d

Overview

Group: SmallGroup(1344,11684)
Rank: 4
Schläfli Type: {8,4,2}
Vertices, edges, …: 84, 168, 42, 2
Order of s₀s₁s₂s₃: 14
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{8,4,2}*672b

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)

s0 := (1,2)(3,6)(4,8)(5,7);;
s1 := (2,5)(4,7)(6,8);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 9,10);;
s3 := (11,12);;
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*s1*s2, s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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