Presentations of 3-manifolds by genuine triangulations

Presentation by a genuine triangulation has the following form (this is a genuine triangulation of the 3-sphere):

facets:=[
[1,2,3,4], [2,5,6,7], [2,3,4,7], [2,3,6,7],
[1,2,3,6], [2,5,6,8], [1,2,6,8], [1,2,4,7],
[2,5,7,8], [1,2,7,8], [1,3,4,7], [1,6,7,8],
[1,3,6,7], [5,6,7,8]
];

The word "facets" is a command word. The numbers 1,2,3, etc. are the names of the vertices of the triangulation. The list of 4-tuples describes the set of tetrahedra of the triangulation, namely, the presence of a certain 4-tuple, say, [1,2,3,4], means that the triangulation contains a (by definition unique) tetrahedron spanning vertices 1, 2, 3, 4.

Theprogram works by building the dual special spine to the triangulation and operating with it. You can immediately view this spine by clicking Information|Show Boundary Curves. In this presentation of the spine, vertex v1 corresponds to the first tetrahedron in the initial list, vertex v2 corresponds to the second one, and so on.

Recall also that each edge of the spine corresponds to gluing between two tetrahedra with a common face. The name of any edge begins with the name of the tetrahedron corresponding to the beginning of the edge and ends with the name of the tetrahedron corresponding to the end of the edge, for example v12v13.

Remark.

If a given description of genuine triangulation is incorrect (i.e. does not really determine a genuine triangulation) then the default error message 'Spine is empty' appears (at the moment, the program does not provide any hints allowing to locate the mistakes in presentations by triangulations).