## Sunday, 8 December 2013

### A Truncated Octahedron & Non-Overlapping Germ-Grain Model Light

Tom Dixon is a pretty cool British company that designs and manufactures lighting and furniture. The company was established in 2002. Tom Dixon launches new collections annually. One of his recent collections, launched at the Salone del Mobile in Milan, is Etch a collection of acid etched brass, copper and stainless steel lights.

The Etch candle holder is in the form of a truncated octahedron about 13 centimetres in diameter. The truncated octahedron is an Archimedean solid with 8 regular hexagon faces and 6 square faces. In this candle holder one face is missing, but the others are pierced with a patterned array of circular holes. Multiple units can be bolted together with small brass nuts and bolts.

The image below shows:

TOP - Tom Dixon's Etch.
MIDDLE - The array of circular holes.
BOTTOM - A truncated Octahedron.

The Tom Dixon website says that these lights are "inspired by the logic of pure mathematics". Although this sounds like a bit of marketing hoopla it is not without merit.

Archimedean solids, such as the truncated octahedron that is the basis of the Etch design, are a venerable subject for mathematical study.

The pattern is a bit more tricksy. I don't have any idea of what, if any, mathematical method Tom Dixon used to create the piercing patterns, but they do remind me a little bit of 2D spatial patterns that can be created using a class of stochastic model known as 'non-overlapping Germ-Grain' models. For those interested Jenny Andersson has a doctoral thesis and published papers on these models including realisations of them (HERE). Another pertinent paper is available on arXiv HERE.

Below is an example of a realisation of a non-overlapping Germ-Grain model from Andersson's thesis. It's not quite the Etch pattern but I can convince myself that the Etch pattern may well be 'inspired' by the logic of this type of pattern.