Edge Unfoldings of Complementary Corner-Chain Prismatoids at Every Positive Height

We prove that a family of convex prismatoids with complementary monotone corner chains admits a nonoverlapping edge unfolding at every positive height. Each chain may have arbitrarily many edges, and the bases may have any relative horizontal placement, including disjoint projections. The positive coordinate directions in the defining frame meet at an angle in [π/2, π), including the orthogonal case. We specify two spanning cut trees consisting entirely of original polyhedral edges and give sufficient metric inequalities that select a nonoverlapping net for every member of the family. The proof combines Pinciu's face-neighborhood nonoverlap theorem with angular separation of an attached triangular fan and a supporting-circle argument separating the upper face from remote side triangles. All developments preserve the Euclidean metric of the original solid.