In this thesis, we define a static analysis by abstract interpretation of memory manipulations. It is based on a new numerical abstract domain, which is able to infer program invariants involving the operators min and max. This domain relies on tropical polyhedra, which are the analogues of convex polyhedra in tropical algebra. Tropical algebra refers to the set R∪{−∞} endowed with max as addit...

Partial generalizations of the theory virtual polyhedra (sometimes under different names) appeared recently in torus manifolds look very from original polyhedra. Such are based on simple arguments homotopy while is integration over Euler characteristic. We explain how these related to classical convex bodies and The paper basically contains no proofs: all proofs details can be found cited liter...

A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears many (but not all) of them can be relaxed to smooth minimal surfaces (under an appropriate smoothing flow, keeping their symmetries). Here we give a complete classification of the cubic polyhedra. Among these are five new infi...

Uniform polyhedra consist of regular faces and congruent vertices. Allowing for nonconvex faces and vertex figures, there are 75 such polyhedra, as well as 2 infinite families of prisms and antiprisms. A recently discovered uniform way of computing their vertex coordinates is the basis for our program to display all of these solids, among which are many beautiful and stunning shapes. We will al...