Edge Unfoldings of Platonic Solids Never Overlap
Takashi Horiyama, Wataru Shoji · 2011
Is every edge unfolding of every Platonic solid overlapfree? The answer is yes. In other words, if we develop a Platonic solid by cutting along its edges, we always obtain a flat nonoverlapping simple polygon. We also give self-overlapping general unfoldings of Platonic solids other than the tetrahedron (i.e., a cube, an octahedron, a dodecahedron, and an icosahedron), and edge unfoldings of some Archimedean solids: a truncated icosahedron, a truncated dodecahedron, a rhombicosidodecahedron, and a truncated icosidodecahedron. 1