I’ve been studying Geometry, specifically polyhedra for over 25 years. I started as an undergraduate at the College of William and Mary, in 1987, when I was given the task of constructing a modular building block system for a sculpture class I was then taking. I dissected a pentagonal prism into a variety o f shapes and built an architectural structure in plaster.
After I graduated, I discovered the Archimedean and Platonic polyhedra and began making paper models of those and their stellations. It was not until 15 years ago that I began inventing my own polyhedra as inspired by the works of Alan Holden in his book, Shapes Space and Symmetry (1971) and The Geometrical Foundations of Natural Structure by Robert Williams as well as Adventures Among the Tori by B.M. Stewart which shaped much of my thinking about the possibilities for polyhedra and Geometry.
One of my first insights into Toric Polyhedra – Nolids with positive genus (or what would become porous materials) was that a Pentaflake could have a three dimensional analog. So, I constructed a Pentaflake Dodecahedron. I then made over forty porous or toric polyhedra. Then, I generallized to the Platonic and Archimedean polyhedra. Exploded polyhedra followed, then Ring/Star and Crown Polyhedra. After that I invented Crinkled Polyhedra as inspired by Henning Hopf’s book Classics in Hydrocarbon Chemistry.
In the early 2000’s, I found Henning Hofp’s book, which more than anything else convinced me of the reciprocal relationship between Geometry and Chemistry. Added to that is the nanoscience revolution along with materials science both of which have informed my interest in Structural Geometry/Nanogeometry/Chemogeometry.
Finally and most recently, I have taken a keen interest in Reticular Chemistry/Geometry and hope to pursue it as it applies to Syndimensional Geometry.
As of 2/15/16, my work on Toric Polyhedra has come to a close. I am now pursuing more global interests in Geometry, Topology, Geometric Topology and Topological Geometry with the idea of providing a systematic method with which to organize and classify objects from both Geometry and Topology.
Within this framework, I will employ as my working methodology findings from Cognitive Science in the form of “Conceptual Blending”. This method enables me and you or anyone else to generate an infinite variety of objects as I will only hint at in the four books I (you and I) propose to write.
These books will provide a system and a systematic way of both classifying existing objects and also generating new ones. Neither is it limited to ontology for it has an epistemological component, as well, as will be seen when I “complete these books. The results can then be applied to the traditionally defined physical sciences such as Chemistry, Physics and the Material Sciences as well as the emerging sciences of Nanophysics, Nanochemistry and Nanomathematics.