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.
O’Rourke, Spiral unfoldings of convex polyhedra, arXiv preprint arXiv:1509.00321
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the polyhedra of revolution.
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Three Archimedean solids and six Catalan solids are classified as always peelable under the new apple peel unfolding definition, with three of each type possible under restrictions and the rest impossible.
citing papers explorer
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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.
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Apple Peel Unfolding of Archimedean and Catalan Solids
Three Archimedean solids and six Catalan solids are classified as always peelable under the new apple peel unfolding definition, with three of each type possible under restrictions and the rest impossible.