La logica dei poliedri

We describe the deep relationship between rational polyhedra, weighted abstract simplicial complexes, and finitely presented MV-algebras - the algebras of finitely axiomatizable theories in Łukasiewicz infinite-valued logic. Combining Alexander's classical stellar machinery with the solution, by Włodarczyk and Morelli, of the weak Oda conjecture on toric varieties, we shall present several results involving classification, measurability, dissectability, and computability.