The minimum illuminating direction set cover problem for a polyhedron seeks the minimum cardinality set of 3-D directions that illuminate the entire polyhedron surface. This thesis introduces a new algorithm for solving such problem. The algorithm includes four steps: (1) Computing sliding planes; (2) Constructing visibility polygons; (3) Conducting overlay of polygons on the unit sphere and (4) Applying greedy algorithm to solve a set cover problem. Results have shown the algorithm gives correct answers to a set of polyhedra. Because the visibility polygons results are exact, the solution of the minimum illuminating direction set cover problem is accurate, though might not be optimal.