[dicccdrq] Fun with geodesics

Consider a game with the following mechanic: one is given a 3D shape, an origin point, a destination point, and an off-

[ubmuixzd] Rubik's cube biomes

Consider a game mechanic consisting of rotating a virtual non-shapeshifting twisty puzzle, which brings certain things,

[hwjkpvhd] Generating points in general position

Start with a coarse square grid within a finite shape.  Pick some of those grid points, perhaps randomly, so that

[jklvnylr] Voronoi cells of distinct shapes

What conditions on the locations of cell centers (and the global boundary, if any) guarantee that the corresponding Vor

[dgyjakxx] Abstract polytopes

Wikipedia has a definition of abstract polyhedra based on partially ordered sets.  However, it seems more natural