Essentially, this is the way to go. There is no standard function to do what you want. However, it suffices to have VERTICES_IN_FACETS and the 2-skeleton of the face lattice. You do not need to compute the entire face lattice. See here for how to compute partial face lattices.

Here is an example: three points in the plane (we use homogeneous coordinates, hence the extra "1" in front): > $V=new VoronoiDiagram(SITES=>[[1,0,0],[1,1,0],[1,0,1]]); > print $V->FACETS; 0 0 0 1 1 -2 0 1 1 0 -2 1 1 0 0 0 The FACETS correspond to the SITES (in the same ordering). The extr...

Your complaint is totally justified. I just changed the code accordingly. Please check [10918].

There are several ways to run polymake in a scripted fashion. Scripts as described above. Observe the slight differences in syntax (as compared to what you just type into the shell). The load_command function. Reads commands from a file line by line. Needs a <return> after each line; allows command ...

You might want to look at http://polymake.org/doku.php/tutorial/coordinates.

Will be done. See #554.

The following is a slight variation/addition to the solution suggested above. Suppose you have a cube and some triangulation. This induces a triangulation of the boundary. $c=cube(3); $t=$c->TRIANGULATION->BOUNDARY; The following (naive) code checks all pairs of facets from the triangulation and the...

Done. Will be part of the next release.

Multigraphs do not exits in polymake yet. But they could be modeled as graphs of type props::graph with edge attributes of type int (to count the number of parallel edges). To avoid ambiguity one should probably restrict those attributes to positive integers. In case that later anyone even needs edg...

You may have to do in application fan.