Unfolding Manhattan Towers

TL;DR

This paper presents an algorithm to unfold Manhattan Towers, a specific class of orthogonal polyhedra, into a nonoverlapping planar shape by cutting along a refined grid of edges.

Contribution

It introduces a novel unfolding algorithm tailored for Manhattan Towers, expanding the class of polyhedra that can be unfolded without overlap.

Findings

Successfully unfolds all Manhattan Towers into planar polygons.

Uses a 4x5x1 grid refinement for edge cuts.

Ensures nonoverlapping planar unfoldings.

Abstract

We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4x5x1 refinement of the vertex grid.