Edge-unfolding nested prismatoids

Abstract

A $3$-Prismatoid is the convex hull of two convex polygons $A$ and $B$ which lie in parallel planes $H_A, H_B\subset\mathbb{R}^3$. Let $A'$ be the orthogonal projection of $A$ onto $H_B$. A prismatoid is called nested if $A'$ is properly contained in $B$, or vice versa. We show that every nested prismatoid has an edge-unfolding to a non-overlapping polygon in the plane.