Two Original-Edge Unfoldings for a Family of Parallelogram-Base Prismatoids at Every Positive Height

We establish two explicit original-edge spanning cut trees for a restricted family of convex prismatoids at every height h > 0: each gives a connected planar development in which the interiors of all complete maximal facets are pairwise disjoint. The lower base is a parallelogram with a distinguished angle in (0, π/2] and possibly unequal side lengths. The entire upper polygon is strictly convex, with two anchored sides parallel to the lower edge directions and a corner chain strictly monotone in the corresponding oblique coordinates; its common anchor length is at least both lower side lengths. Both unfoldings preserve the genuine quadrilateral lateral facets without diagonal cuts. Pinciu's face-neighbourhood theorem controls the upper face and its direct edge-neighbours; height-dependent separator inequalities, a whole-bottom support-line argument, and a complete face-pair analysis handle the remaining triangles and lower base. An explicit rational family has arbitrarily many vertices and strictly disjoint horizontal projections of the bases.