Zonal selection produces perfect ordering success on the 120-cell (1440/1440 pairs) but every resulting net self-intersects in 3D, while the 600-cell fails under both rules and the spiral rule underperforms on most tested solids.
Apple Peel Unfolding of Archimedean and Catalan Solids
1 Pith paper cite this work. Polarity classification is still indexing.
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Pith paper citing it
abstract
We consider a new treatment for making polyhedron nets referred to as ``apple peel unfolding'': drawing the nets as if we were peeling off appleskins. We define apple peel unfolding strictly and implement a program that derives the sequential selection of the polyhedral faces for a target polyhedron in accordance with the definition. Consequently, the program determines whether the polyhedron is peelable (can be peeled completely). We classify Archimedean solids and their duals (Catalan solids) as perfect (always peelable), possible (peelable for restricted cases), or impossible. The results show that three Archimedean and six Catalan solids are perfect, and three Archimedean and three Catalan ones are possible.
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cs.CG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Apple-Peel Unfolding in Three and Four Dimensions: Spiral and Zonal Selection Rules
Zonal selection produces perfect ordering success on the 120-cell (1440/1440 pairs) but every resulting net self-intersects in 3D, while the 600-cell fails under both rules and the spiral rule underperforms on most tested solids.