3D realization of two triangulations of a onvex polygon

Abstract

We study the problem of construction of a convex 3-polytope whose (i) shadow boundary has n vertices and (ii) two hulls, upper and lower, are isomorphic to two given triangulations of a convex n-gon. Barnette [℄ D. W. Barnette. Projections of 3-polytopes. Israel J. Math., 8:304{308, 1970] proved the existence of a convex 3-polytope in general case. We show that, in our case, a polytope can be constructed using an operation of edge creation