Polytope of Type {6,6} with group SmallGroup(720,767)

Overview

Group: SmallGroup(720,767)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 60, 180, 60
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

3-fold

{6,6}*240a

6-fold

{6,6}*120

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

30 facets

30 of {6}*12

30 vertex figures

30 of {6}*12

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

30 facets

30 of {6}*12

33 vertex figures

27 of {6}*12
6 of {3}*6

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0> of order 3

24 facets

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

20 vertex figures

20 of {6}*12

P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 5

12 facets

12 of {6}*12

12 vertex figures

12 of {6}*12

P/N, where N=<(s1*s2)^3, (s0*s2*s1)^3> of order 6

12 facets

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

13 vertex figures

6 of {3}*6
7 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.