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.

翻译：苹果皮展开是一种贪婪算法，以螺旋顺序每次选取多面体（或多胞体）的一个面（或胞腔），生成类似于连续单条剥下苹果皮的展开图。我们定义了两种面选取规则——RS（螺旋规则：最小有向行列式，即最陡顺时针转向）和RZ（区域规则：沿剥皮轴的最大坐标）——并系统评估了它们在(i)五种柏拉图立体、(ii)十三种阿基米德立体和(iii)六种正则凸四胞体上的展开成功率。主要贡献在于将每个立体分为三类：*完全*（每个起始对均产生完整展开图）、*可能*（至少有一个起始对成功）或*不可能*（无起始对成功），同时通过等变性论证表明，面对称立体仅限于0/100%的二分情况。在大多数情形中，RZ规则实现了最高成功率；对于正则四胞体，它是唯一能在120胞腔上产生非零结果的规则，并取得了*完全*结果（1,440/1,440起始对）。我们指出，*排序成功*（完成贪婪遍历）与*几何有效性*（三维实现中无自交）是不同的：每个120胞腔的排序均产生自交的三维展开图，因此尽管其排序结果完美，但120胞腔的有效三维展开图数量为零。600胞腔在所有测试规则下均为*不可能*。