Post #3078243

I built a paper model of a great dodecahedron. The net consists of 12 pentagonal "flower" shapes, each in a different color. What makes this particular net interesting is that it also serves as a net for a regular dodecahedron: the same flat pattern can be folded into either shape. This dual property is quite rare: most dodecahedron nets do not work as great dodecahedron nets. With an arbitrary net, two faces will typically end up in the same position while another face is missing entirely. Folding it into the great dodecahedron is the challenging part: the faces penetrate and interlace with one another, requiring the paper to be bent and woven together. The first part of this video: https://mathstodon.xyz/@nanma80/109450926293000017 shows how this net folds into a dodecahedron and then into a great dodecahedron, when the faces are allowed to pass through each other. This paper model is my attempt to bring the simulation into the physical world.