Can every convex vertex be unfolded into a flat sheet?

Ideas & Philosophy · Published 7 October 2026 Swipe more like this →

In short: This lecture explores the mathematical limits of unfolding polyhedra, examining why certain convex vertices cannot be flattened and how complex orthogonal shapes are handled.

The session investigates topologically convex vertex-ununfoldable cases, addressing the geometric constraints that prevent certain shapes from being unfolded without overlapping. It also explores methods for unfolding orthogonal polyhedra, specifically through the application of heavy-light decomposition. Additionally, the lecture provides a review of Cauchy's Rigidity Theorem.

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