## 29 March, 2010

### A Three Dimensional Problem

Introducing the Soma Strand

These images are from a paper forthcoming to the Shape journal, as part of the "A Structure of Diagrams" series. Here diagrams and models were used to solve a complex three dimensional problem based on tessellation.

This case was to do with a self designed form which I had named the Soma Strand (after Piet Hein’s “Soma delicious Soma”).
Long before the tessellation problem outlined above, I had to design the original form. This, in itself, took a great deal of time and model making, but what finally emerged was an infinite strand, with a re-entrant form, and congruent, singly re-entrant hexagonal faces (with 90o and 270o angles only). It soon became clear (after making a bundle of these strands, that they definitely tessellated to fill three dimensional space completely.
Careful model-making had established this exciting property, but, it must be said that cardboard, glue and bits of wooden dowling (without which the strands were impossible to construct) are not the ideal materials to facilitate detailed studies in the area of volume filling stacking, particularly of such difficult (and indeed infinite) strands. Attempts at solving the problem using 3D graphics packages were soon abandoned, as these so-called tools, may deal with three dimensions, but are generally NOT designed for meaningful and revealing visualisations essential to the designer and creator of new things. You just couldn’t see what you were doing, and the figures soon became unintelligible. In addition to the complexity, that package had not helped me to adjust units effectively and lock them into the required precise positionings. Attempts at colouring to get some order out of the chaos only led to an obscuring of one part of the figure by another. I knew exactly what I wanted to do, but those facilities were simply not available.
As a last resort, I went all the way back to an ancient (and primitive) 2D drawing package that I had used for many years (De Luxe Paint 2).