Study of Parametric Dodecaherdon in OpenSCAD
Description
I've been a long-time fan of dodecahedrons and I've been messing with trigonometry a lot lately so I thought I'd try my hand at making on and while I'm at it I might as well draw numbers on it and help someone make a 200mm D-12 die. I'm trying to figure out how to solve for dihedral angles especially of regular polyhedrons like the dodecahedron but also really the combination of any number of angles closing a vertex of three or more plans to form a closed mesh. Someone figured this stuff or using trigonometry or linear alegra or whatever it was that the Buckminster Fullers of the world use to generate geodesics and suched. I really need to go back to school, clearly I'm learning a marketable skill here. How does a building contractor join a 1:1 pitch roof to a 1:2 pitch roof that meets at a 120 angle? HOW?! I did learn that the dihedral angle of a dodecahedron was the arc-cosine of negative one over the square root of five ... but why? how? when? who?! Anyway here's a parametric Customizer I wrote in OpenSCAD and a few STL examples including a 200mm D-12 twleve-sided die ... enjoy!
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