Polytope of Type {6,6} with group SmallGroup(1440,5842)

Overview

Group: SmallGroup(1440,5842)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 120, 360, 120
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual

Quotients maximal quotients in bold

2-fold

{6,6}*720a

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*(s2*s1)^2*(s0*s2*s1)^3> of order 2

60 facets

60 of {6}*12

60 vertex figures

60 of {6}*12

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

60 facets

60 of {6}*12

60 vertex figures

60 of {6}*12

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

44 facets

38 of {6}*12
6 of {2}*4

40 vertex figures

40 of {6}*12

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

40 facets

40 of {6}*12

44 vertex figures

6 of {2}*4
38 of {6}*12

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2*s1, (s0*s2*s1)^2*s0*(s2*s1)^2*s0*s2*s1> of order 6

22 facets

19 of {6}*12
3 of {2}*4

20 vertex figures

20 of {6}*12

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s1*s2*s1, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1*s2> of order 6

20 facets

20 of {6}*12

22 vertex figures

19 of {6}*12
3 of {2}*4

P/N, where N=<(s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s1*s2> of order 9

16 facets

12 of {6}*12
4 of {2}*4

16 vertex figures

4 of {2}*4
12 of {6}*12

Representations

Permutation Representation (GAP)

s0 := (3,5);;
s1 := (2,3)(4,6);;
s2 := (1,4)(2,6)(3,5)(7,8);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

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

References

None.

to this polytope.