Robert L. Read
That a number of physical objects, such as the Platonic solids, can generate helices, has been published in scattered papers. However, the math to determine the radius and rate of rotation from the underlying object has never been studied. We have proved an observation by Eric Lord based on Chasles’ Theorem and provided algorithms for this, which as allows us to complete enumerate, and render interactively in 3D, the set of 28 unique Platonic helices. This work allows chemist and mechanical engineers to relate the shape of basic objects to the helices they produce when strung together, allowing either the objects to be deduced from the helix or designed from a desired helix.
During the 2018 Public Invention Mathathon, the participants noticed the odd fact that every repeated rule let to physical structure resembling a helix. Following up on this observation led us to our first inklings that all object produce helices. Through several months we did the research to produce a fully interactive 3D rendering system that allows one to explore this relationship mathematically. Along the way, this net caught the “zoo” of all possible Platonic helices. We are attempting to complete the academic publication now.
Main Interactive Page: https://pubinv.github.io/segmented-helixes/index.html