Polytope of Type {8,6} with group SmallGroup(384,5602)

Overview

Group: SmallGroup(384,5602)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 32, 96, 24
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{4,6}*192a

8-fold

{4,6}*48c

16-fold

{4,3}*24

Covers minimal covers in bold

2-fold

3-fold

{8,18}*1152c

5-fold

{8,30}*1920c

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

12 facets

12 of {8}*16

16 vertex figures

16 of {6}*12

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

12 facets

12 of {8}*16

20 vertex figures

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

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

6 facets

6 of {8}*16

8 vertex figures

8 of {6}*12

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

6 facets

6 of {8}*16

12 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.