Polytope of Type {6,6} with group SmallGroup(384,5602)

Overview

Group: SmallGroup(384,5602)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 32, 96, 32
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

2-fold

{6,6}*192a

16-fold

{3,3}*24

Covers minimal covers in bold

2-fold

{6,6}*768e

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)^3> of order 2

20 facets

8 of {3}*6
12 of {6}*12

20 vertex figures

12 of {6}*12
8 of {3}*6

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

16 facets

16 of {6}*12

16 vertex figures

16 of {6}*12

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

12 facets

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

12 vertex figures

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

P/N, where N=<s0*(s1*s2)^2*s1*s0*s2, s0*s2*(s1*s0)^2*s1*s2> of order 4

12 facets

4 of {6}*12
8 of {3}*6

12 vertex figures

4 of {6}*12
8 of {3}*6

P/N, where N=<(s0*s1)^3, (s1*s2)^3, s0*(s1*s2)^2*s1*s0*s2> of order 8

7 facets

6 of {3}*6
1 of {6}*12

7 vertex figures

6 of {3}*6
1 of {6}*12

P/N, where N=<(s0*s1)^3, s0*s2*s1*s0*s1*s2> of order 24

3 facets

2 of {3}*6
1 of {2}*4

3 vertex figures

2 of {3}*6
1 of {2}*4

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.