Polytope of Type {4,8} with group SmallGroup(128,327)

Overview

Group: SmallGroup(128,327)
Rank: 3
Schläfli Type: {4,8}
Vertices, edges, …: 8, 32, 16
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

11-fold

13-fold

14-fold

15-fold

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)^2> of order 2

12 facets

8 of {2}*4
4 of {4}*8

4 vertex figures

4 of {8}*16

Representations

Permutation Representation (GAP)

s0 := ( 5, 6)( 7, 8)(13,14)(15,16);;
s1 := ( 5, 7)( 6, 8)( 9,13)(10,14)(11,15)(12,16);;
s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);;
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, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(16)!( 5, 6)( 7, 8)(13,14)(15,16);
s1 := Sym(16)!( 5, 7)( 6, 8)( 9,13)(10,14)(11,15)(12,16);
s2 := Sym(16)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);
poly := sub<Sym(16)|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, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.