Open Problems on Polytope Reconstruction

. We describe some open algorithmic problems relatedto constructing 3-dimensional polytopes from limitedinformation.Introduction. There are several dierent ways to specifyconvex polytopes in three dimensions. One obviousexplicit representation is a list of the vertex coordinatesand connectivity information between the vertices,edges, and facets. But not all this information is necessary.For example, we can reconstruct the explicitrepresentation given only the vertex coordinates;...