Some indecomposable polyhedra
David T. Yost · Optimization · 2007
We complete the classification, in terms of decomposability, of all combinatorial types of polytopes with 14 or fewer edges. Recall that a polytope P is said to be decomposable if it is equal to a Minkowski sum of two polytopes Q and R which are not similar to P. Our main contribution here is to consider the 42 types of polyhedra with 8 faces and 8 vertices. It turns out that 34 of these are always indecomposable, and 5 are always decomposable. The remaining 3 are ambiguous, i.e. each of them has both decomposable and indecomposable geometric realizations.