What is a buckyball? Part 3: Fullerenes

In the previous post we saw how we could project polyhedra into the plane, and use some simple properties about planar graphs to classify all the possible Platonic solids. In this post we’ll finally get to the buckyball, by considering a less restrictive class of polyhedra: the fullerenes. The Platonic solids were extremely regular: every …

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What is a Buckyball? Part 2: Projection

How can we represent a 3-dimensional object such a cube in only 2-dimensions, such as on a flat piece of paper? This is the problem of projection, and it inevitably introduces inaccuracies. Different choices of perspective will alter what features survive the projection process. For instance, a perfect cube has all faces square, with corner …

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What is a Buckyball? Part 1: Planar Graphs

Earlier this year I was involved with the construction of the `Giant 4D Buckyball‘, as part of the University of Edinburgh’s Innovative Learning Week. The sculpture was actually of something rather more complicated – the Cantitruncated 600-cell – but buckyballs (in various representations) were a fundamental building block. So, what exactly are they? Julia’s description …

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2014 Joint Mathematics Meetings Art Exhibition

Some of my work will once again be included in the art exhibition at the Joint Mathematics Meetings– a selection of stills from my video project x<–>t, which I described on my main site here. The image above is a more recent rendering using the same ‘strip photography’ technique: it captures the changing behaviour through …

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For the 2013/14 academic year I’ll be back at the University of Edinburgh, to take part in the Operational Research MSc. This page will track my progress through the course!

The benign dictatorship of the London Underground

Earlier today I spotted this video, featuring the stand-up mathematician Matt Parker and all-round interesting person Tom Scott exploring some oddities of the tube: Matt’s ability to beat Tom around the network depended on local knowledge of hidden shortcuts. You might wonder why these quicker options aren’t indicated by signs, but as they explain in …

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Lehmer’s Conjecture for Hermitian Matrices over the Eisenstein and Gaussian Integers

My third paper on the Mahler measure problem has been accepted by the Electronic Journal of Combinatorics, and is available here freely under the E-JC’s open access policy. This is joint work with Gary Greaves, and completes the proof of Lehmer’s conjecture for matrices with entries from rings of integers of quadratic extensions: a project …

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‘Introduction to Graph Theory’ Lecture Materials

I have now completed a series of introductory lectures on Graph Theory, for 3rd/4th year students at the University of Bristol. A set of written notes plus (less usefully) my slides are mirrored here. One student declared this to be “[the] most interesting course I have taken at Bristol Uni”, so take a look to …

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JMM 2013 Highlights

Earlier this month I attended the 2013 Joint Mathematics Meetings, trading freezing Britain for sunny San Diego! This was the 119th annual meeting of the American Mathematical Society, the 96th of the Mathematical Association of America, my third trip to the US for a JMM, and the first at which I’ve given a talk. There …

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