Polytope of Type {12,6} with group SmallGroup(480,951)

Overview

Group: SmallGroup(480,951)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 40, 120, 20
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Related Polytopes

Constructions

Facet of

{12,6,2} ·960

Vertex figure of

Quotients maximal quotients in bold

2-fold

{6,6}*240b

4-fold

{6,6}*120

Covers minimal covers in bold

2-fold

3-fold

{12,6}*1440a

4-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

10 facets

10 of {12}*24

20 vertex figures

20 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.