Alexandrov, A. D. (2005), Convex Polyhedra, Springer Monographs in Mathematics, Berlin: Springer-Verlag, ISBN3-540-23158-7, MR2127379; see in particular Chapter 6, Conditions for Congruence of Polyhedra with Parallel Faces, pp. 271–310, and Chapter 7, Existence Theorems for Polyhedra with Prescribed Face Directions, pp. 311–348