This paper describes algorithms for computing global accessibility cones for various faces (i.e., the set of directions from which faces are accessible) in a polyhedral object. We describe exact mathematical conditions and the associated algorithm for determining the set of directions from which a planar face with triangular boundary is inaccessible due to another face in the object. By utilizing the algorithm to compute the exact inaccessibility region for a face, we present algorithms for computing global accessibility cones for various faces in the object. These global accessibility cones are represented in a matrix structure and can be used to support a wide variety of accessibility queries for the object. We provide several examples to show computational performance of our algorithm.