BI-CYCLIC 4-POLYTOPES

In a previous paper [2] we studied the facial structure of convex hulls of certain curves that lie on the torus {Mathematical expression} In this paper we use the results of [2] to study structure of convex hulls of certain finite subsets of T 2. Specifically, we study the combinatorial structure of the polytopes whose vertex sets are finite subgroups of T 2. Such a subgroup may be represented by Λ/Z 2, where Λ ⊇Z 2 is some planar geometric lattice. We shall show how the facial structure of the polytope may be read directly off the lattice Λ. We call these polytopes bi-cyclic polytopes; a study of their properties is under preparation. © 1990 Hebrew University.