Self-dual polyhedra of given degree sequence

Given vertex valencies admissible for a self-dual polyhedral graph, we describe an algorithm to explicitly construct such polyhedron. Inputting in the permutations of degree sequence can give rise non-isomorphic graphs. As application, find as function n ≥ 3 minimal number vertices polyhedron with at least one i each ≤ n, and polyhedra. Moreover, construction non-self-dual graphs order i-gonal face n. Another application is rigidity theory, since constructed families polyhedra are generic circuits, globally rigid plane.