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Products of simplices, called simplotopes, and their triangulations arisenaturally in algorithmic applications in game theory and optimization. Wedevelop techniques to derive lower bounds for the size of simplicial covers andtriangulations of simplotopes, including those with interior vertices. Weestablish that a minimal triangulation of a product of two simplices is givenby a vertex triangulation, i.e., one without interior vertices. For products ofmore than two simplices, we produce bounds for products of segments andtriangles. Aside from cubes, these are the first known lower bounds fortriangulations of simplotopes with three or more factors, and our techniquessuggest extensions to products of other kinds of simplices. We also construct aminimal triangulation of size 10 for the product of a triangle and a squareusing our lower bound.

A lower bound technique for triangulations of simplotopes