Polytope of Type {6,6,3} with group SmallGroup(1920,240996)

Overview

Group: SmallGroup(1920,240996)
Rank: 4
Schläfli Type: {6,6,3}
Vertices, edges, …: 40, 160, 80, 5
Order of s₀s₁s₂s₃: 5
Order of s₀s₁s₂s₃s₂s₁: 3
Also known as: if this polytope has a name.

Special Properties

Orientable

Quotients maximal quotients in bold

16-fold

{3,3,3}*120

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*(s1*s0*s2)^3*s1*s2> of order 2

5 facets

1 of {6,6}*192a
4 of 2-fold non-regular quotient of {6,6}*384a

24 vertex figures

16 of {6,3}*48
8 of {3,3}*24

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.