It is pointed out that, in making automatic the processes of machine design by means of man-machine interaction, the machine lacks the capability of generating the shape of machine parts. To overcome this difficulty in principle, the paper presents a topological method of generating convex polyhedra. As an instruction from man the edge-vertex table (k, λ
k|k=3, 4, ..., r, where k: number of edges gathering into a vertex, λ
k : number of k-edged vertex) is proposed. When the machine receives the edge-vertex table, it generates all of the mutually different linear dual graphs on convex polyhedra, where the graphs have Hamiltonian cycles. The fundamental theory for the above process is contained.
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