The Megahedron

Continuing to experiment with the irregular tetrahedral tri-modules used in Meg's icosahedron, we started work a couple of weeks ago on the Megahedron. We came up with the idea by observing that the cube is actually built by connecting three tri-modules at each super-vertex, then the octahedron having four tri-modules per, and the icosahedron having five.

Our plan was to try it next with six tri-modules at each super-vertex. However we quickly ran into a degeneracy where the resulting surface was flat, completely irretrievably flat. Motivated to find something cool to do nonetheless with the massive quantity of tri-modules already produced by the team, Mommy stared hard at the pinterest model and noticed that some of the super-vertices only had five tri-modules adjoining rather than six. Extending the symmetry in the only way possible, we finally found a way to close our Megahedron into a fancy stellated pentakis dodecahedron.Læs mere