arXiv subjects

Takashi Yoshino

Publications and source records attributed to Takashi Yoshino.

4 recordsLinked to original sources

arXiv2026

Apple-Peel Unfolding in Three and Four Dimensions: Spiral and Zonal Selection Rules

Apple-Peel Unfolding is a greedy algorithm that selects the faces (or cells) of a polyhedron (or polytope) one at a time in a spiral order, producing a net analogous to peeling an apple in a single continuous strip. We define two face-selection rules -- RS (Spiral rule: minimum signed determinant, i.e.\ sharpest clockwise turn) and RZ (Zonal rule: maximum coordinate along the peeling axis) -- and systematically evaluate their unfolding success rates on (i)~the five Platonic solids, (ii)~the thirteen Archimedean solids, and (iii)~the six regular convex 4-polytopes. A principal contribution is a three-way classification of each solid as \emph{Perfect} (every starting pair yields a complete net), \emph{Possible} (at least one pair succeeds), or \emph{Impossible} (no pair succeeds), together with an equivariance argument showing that face-transitive solids are confined to the $0/100\%$ dichotomy. RZ achieves the highest success rates in most cases; for the regular 4-polytopes it is the only rule yielding non-zero results for the 120-cell, where it achieves a Perfect result (1,440/1,440 pairs). We note that \emph{ordering success} (completing the greedy traversal) and \emph{geometric validity} (no self-intersection in the 3D realization) are distinct: every 120-cell ordering produces a self-intersecting 3D net, so the 120-cell has zero valid 3D nets despite its Perfect ordering result. The 600-cell is Impossible under all rules tested.

cs.CG↗

arXiv2026

Spherical Geometrical Bases of Spherical Origami

This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and three-dimensional folding of spherical sheets in space. For origami on $\mathbb{S}^2$, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry. For three-dimensional folding, equidistant curves are introduced as fold curves, replacing geodesics and enabling a richer family of folds. The framework is validated by successfully constructing computer graphics of spherical origami birds, demonstrating both the theoretical completeness and practical utility of the proposed approach.

cs.CG↗

arXiv2026

Apple Peel Unfolding of Archimedean and Catalan Solids

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.

cs.CG↗

arXiv2016

Optical signatures of low spin Fe3+: a new probe for the spin state of bridgmanite and post-perovskite

Iron spin transition directly affects properties of lower mantle minerals and can thus alter geophysical and geochemical characteristics of the deep Earth. While the spin transition in ferropericlase has been vigorously established at P ~ 60 GPa and 300 K, experimental evidence for spin transitions in other rock-forming minerals, such as bridgmanite and post-perovskite, remains controversial. Multiple valence, spin, and coordination states of iron in bridgmanite and post-perovskite are difficult to resolve with conventional spin-probing techniques. Optical spectroscopy, on the other hand, is sensitive to high/low spin ferrous/ferric iron at different sites; thus, it can be a powerful probe for spin transitions. Here we establish the optical signature of low spin Fe3+O6, a plausible low spin unit in bridgmanite and post-perovskite, by optical absorption experiments in diamond anvil cells. We show that the optical absorption of Fe3+O6 in NAL (new aluminous phase) is very sensitive to the iron spin state and represents a model behavior of bridgmanite and post-perovskite in the deep lower mantle across a spin transition. Specifically, an absorption band centered at ~ 19000 cm-1 is characteristic of the 2T2g to 2T1g (2A2g) transition in low spin Fe3+ in NAL at 40 GPa. This new spectroscopic information constrains the crystal field splitting energy of low spin Fe3+ to ~ 22200 cm-1 which we also independently confirm by our first-principles calculations. Together with available information on the electronic structure of Fe3+O6-compounds, we constrain the spin-pairing energy of Fe3+ in an octahedral field to ~ 20000-23000 cm-1. This implies that octahedrally-coordinated Fe3+ in bridgmanite is low spin at P > ~ 40 GPa.

physics.geo-ph↗