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.

翻译：我们提出一种制作多面体展开图的新方法，称之为"苹果皮展开"：即如同削苹果皮般绘制展开图。我们严格定义了苹果皮展开方法，并实现了一个程序，该程序根据定义推导出目标多面体面的顺序选择。进而，程序可判定该多面体是否可剥（是否能被完全剥开）。我们将阿基米德体及其对偶（卡塔兰体）分类为：完美（始终可剥）、可能（在特定条件下可剥）或不可能。结果表明，三种阿基米德体和六种卡塔兰体属于完美，三种阿基米德体和三种卡塔兰体属于可能。