Constructability of trip-lets

A trip-let is an object as shown on the cover of Hofstadter’s book Gödel, Escher, Bach: a solid, threedimensional object that, when viewed from three orthogonal directions, shows three different letters. In this paper we consider two problems related to the construction of such objects for a given set of three letters. First, we want to know whether the silhouettes of the object correspond to the letters we used to make the object. Second, we are interested in the connectedness of the final object: does it fall apart during construction? We obtain results on the combinatorial complexity of objects and silhouettes for letters given as general or rectilinear polygons with holes, and give algorithms to solve the problems efficiently for the rectilinear case.