# Voronoi tessellations in architecture

A colleague just sent me this photo of a colourful building on the Gold Coast. The building is the new Home of the Arts (HOTA) Gallery, as detailed here. It is covered in a Voronoi tessellation. I described this very useful geometrical object in a previous post.

A casual Google reveals that other buildings have Voronoi-inspired architecture. For example, The Fry building at the University of Bristol in Britain, which fittingly houses the mathematics department.

The building for the Alibaba headquarters in China also evokes Voronoi imagery. But those Voronoi constructions do no feature the colours of the HOTA Gallery, which is reminiscent of diagrams produced by scientific plotting packages.

(Of course I don’t mind the odd Voronoi tesselation. For example, a couple of months ago I set for my website image a Voronoi tesselation, created by the Franco-German artist Plaisance Puisatier. And the cover of a book I co-wrote has a diagram based on the signal-to-interference ratio, which can be considered as a generalization of a Voronoi tessellation.)

## Mathematical buildings

Another building that employs an interesting geometrical object is RMIT’s Storey Hall, located in Melbourne. It features Penrose tiling, which is an example of a non-periodic tiling. Loosely speaking, that means if you tile an infinite plane with a given a set of tiles, then no translation of the plane will yield the same pattern again. The Penrose tiling is also inside the building, as you can see on this website.

On topic of non-periodic tiling, the buildings at Federation Square in Melbourne are covered by pinwheel tiling, as shown on this mathematics website, which is also non-periodic. According to Wikipedia, Charles Radin proposed this tiling based on a construction by the late and famous John Conway who died earlier this year, being yet another victim of the pandemic.

## Mathematical architects

While writing this post, I noticed that both the HOTA Gallery and Storey Hall were designed by ARM Architecture. Some of their other buildings have a geometrical aspect. Clearly they have a mathematical inclination.

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