Sunday, November 8, 2015
My understanding is that designing geodesic domes is nontrivial because there are so many choices. Here I present a way to find every dome up to complexity. Consider all sections of all spaces up to complexity. The cospace of the vertices on one of those sections has all planes through a point. Designate that point the center of a dome. The surface of the dome is the round space as defined in the "Coincidence" post. Note that not every region of the round space need be a facet of the dome. Some dome facets can be super-regions in the round space.