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 $A^{\prime }$ be the orthogonal projection of $A$ onto $H_B$. A prismatoid is called nested if $A^{\prime }$ 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.

arXiv comment15 pages, 7 figures