Polytope of Type {5,2,4,4,2} with group SmallGroup(640,19898)

Overview

Group: SmallGroup(640,19898)
Rank: 6
Schläfli Type: {5,2,4,4,2}
Vertices, edges, …: 5, 5, 4, 8, 4, 2
Order of s₀s₁s₂s₃s₄s₅: 20
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,5,2,4,4,2} ·1280

Quotients maximal quotients in bold

2-fold

4-fold

{5,2,2,2,2}*160

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP)

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,11);;
s3 := ( 6, 7)( 8,10)( 9,12)(11,13);;
s4 := ( 7, 9)( 8,11);;
s5 := (14,15);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

s0 := Sym(15)!(2,3)(4,5);
s1 := Sym(15)!(1,2)(3,4);
s2 := Sym(15)!( 7, 8)( 9,11);
s3 := Sym(15)!( 6, 7)( 8,10)( 9,12)(11,13);
s4 := Sym(15)!( 7, 9)( 8,11);
s5 := Sym(15)!(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma)

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