Polytope of Type {4,6} with group SmallGroup(192,955)

Overview

Group: SmallGroup(192,955)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 16, 48, 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

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,4,6} ·384

Quotients maximal quotients in bold

4-fold

{4,6}*48c

8-fold

{4,3}*24

Covers minimal covers in bold

2-fold

3-fold

{4,18}*576a

4-fold

5-fold

{4,30}*960a

6-fold

7-fold

{4,42}*1344a

9-fold

{4,54}*1728a

10-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*s2*s1*s0*s1*s2> of order 2

12 facets

12 of {4}*8

8 vertex figures

8 of {6}*12

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

14 facets

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

8 vertex figures

8 of {6}*12

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

12 facets

12 of {4}*8

10 vertex figures

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

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

8 facets

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

4 vertex figures

4 of {6}*12

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

9 facets

3 of {4}*8
6 of {2}*4

4 vertex figures

4 of {6}*12

P/N, where N=<(s1*s2)^3, s0*(s1*s2)^2*s1*s0*s2> of order 4

6 facets

6 of {4}*8

6 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.