Polytope of Type {2,10,2,6} with group SmallGroup(480,1207)

Overview

Group: SmallGroup(480,1207)
Rank: 5
Schläfli Type: {2,10,2,6}
Vertices, edges, …: 2, 10, 10, 6, 6
Order of s₀s₁s₂s₃s₄: 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 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-fold

{2,10,2,2}*160

4-fold

{2,5,2,3}*120

5-fold

{2,2,2,6}*96

6-fold

{2,5,2,2}*80

10-fold

{2,2,2,3}*48

15-fold

{2,2,2,2}*32

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP)

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);;
s3 := (15,16)(17,18);;
s4 := (13,17)(14,15)(16,18);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(18)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,12);
s3 := Sym(18)!(15,16)(17,18);
s4 := Sym(18)!(13,17)(14,15)(16,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

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