An Algorithm for Constructing 3D Struts

A simple robust "strut algorithm" is presented which, when given agraph embedded in 3D space, thickens its edges into solid struts.Various applications, crystallographic and sculptural, are shown inwhich smooth high-genus forms are the output. A toolbox of algorithmictechniques allow for a variety of novel, visually engaging forms thatexpress a mathematical aesthetic. In sculptural examples, hyperbolictessellations in the Poincar\'e plane are transformed in several ways tothree-dimensional networks of edges embodied within a plausibly organicorganization. By the use of different transformations and adjustableparameters in the algorithms, a variety of attractive forms result. Thetechniques produce watertight boundary representations that can bebuilt with solid freeform fabrication equipment. The final physicaloutput satisfies the "coolness criterion," that passers by will pickthem up and say "Wow, that's cool!"