|Abstract A simple robust "strut algorithm" is presented which, when given a
graph embedded in 3D space, thickens its edges into solid struts.
Various applications, crystallographic and sculptural, are shown in
which smooth high-genus forms are the output. A toolbox of algorithmic
techniques allow for a variety of novel, visually engaging forms that
express a mathematical aesthetic. In sculptural examples, hyperbolic
tessellations in the Poincar\'e plane are transformed in several ways to
three-dimensional networks of edges embodied within a plausibly organic
organization. By the use of different transformations and adjustable
parameters in the algorithms, a variety of attractive forms result. The
techniques produce watertight boundary representations that can be
built with solid freeform fabrication equipment. The final physical
output satisfies the "coolness criterion," that passers by will pick
them up and say "Wow, that's cool!"