Polytope of Type {12,4} with group SmallGroup(288,889)

Overview

Group: SmallGroup(288,889)
Rank: 3
Schläfli Type: {12,4}
Vertices, edges, …: 36, 72, 12
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 6
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

{6,4}*144

4-fold

{6,4}*72

9-fold

{4,4}*32

18-fold

36-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-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)^3*s2*(s1*s0)^2*s1*s2> of order 2

6 facets

6 of {12}*24

18 vertex figures

18 of {4}*8

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

4 facets

4 of {12}*24

12 vertex figures

12 of {4}*8

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

8 facets

6 of {4}*8
2 of {12}*24

12 vertex figures

12 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.