Unfolding Polycubes with Orthogonally Convex Layers
Abstract
A polycube is an orthogonal polyhedron composed of unit cubes glued together along entire faces, and homeomorphic to a sphere. A layer of a polycube refers to the portion lying between two horizontal cross-sections spaced one unit apart. We present an unfolding algorithm that flattens any polycube with orthogonally convex layers into a single, non-overlapping planar piece. The algorithm makes cuts only along cube edges-that is, it is an edge unfolding.
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