David Yost

Decomposability of Polytopes

A known characterization of the decomposability of polytopes is reformulated in a way which may be more computationally convenient, and a more transparent proof is given. New sufficient conditions for indecomposability are then deduced, and illustrated with some examples.

On the Reconstruction of Polytopes

Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its 1-skeleton. Call a vertex of a d-polytope nonsimple if the number of edges incident to it is more than d. We show that (1) the face lattice of any d-polytope with at most two nonsimple vertices is determined by its 1-skeleton; (2) the face lattice of any d-polytope with at most

Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation

d-2

A universal modulus for normed spaces

d-2 nonsimple vertices is determined by its 2-skeleton; and (3) for any

The Excess Degree of a Polytope

d>3

More Indecomposable Polyhedra

d>3 there are two d-polytopes with