Common Nets of (Regular) Polyhedra
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In Chap. 3, we consider box, which is one of the most natural shapes in our daily life. From the viewpoint of mathematics, we have some other natural shapes. For example, we have five regular polyhedra which have been investigated since Archimedean’s period. However, surprisingly, they are not yet well investigated from the viewpoint of the unfolding. For example, it is not known that two regular polygons have a common net. That is, we do not know whether there is a polygon that can fold to two or more regular polyhedra. We give positive and negative results related to this interesting open problem.