Polytope of Type {4,2,4} with group SmallGroup(64,226)

Overview

Group: SmallGroup(64,226)
Rank: 4
Schläfli Type: {4,2,4}
Vertices, edges, …: 4, 4, 4, 4
Order of s₀s₁s₂s₃: 4
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat
Self-Dual

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

{2,2,2}*16

Covers minimal covers in bold

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Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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