Polytope of Type {3,6,6} with group SmallGroup(1440,5849)

Overview

Group: SmallGroup(1440,5849)
Rank: 4
Schläfli Type: {3,6,6}
Vertices, edges, …: 5, 60, 120, 30
Order of s₀s₁s₂s₃: 10
Order of s₀s₁s₂s₃s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Orientable

Quotients maximal quotients in bold

2-fold

{3,3,6}*720

3-fold

{3,6,6}*480

6-fold

12-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*(s2*s3)^2*s2*s1*s0*s3> of order 2

15 facets

15 of {3,6}*48

5 vertex figures

5 of 2-fold non-regular quotient of {6,6}*288b

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.