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This shows how the dodecahedron, a shape with 12 pentagon faces, can be distorted so that it can be drawn with no lines crossing.  In fact any convex polyhedron has this property (loosely ‘convex’ means no dents or spikes). Related is the fact that for convex polyhedra the number of vertices, minus the number of edges, plus the number of faces is always 2. Here that is 20 red vertices - 30 edges + 12 faces = 2. Can you draw a cube with no lines crossing, and does the formula work add up to 2? [more] [code]

This shows how the dodecahedron, a shape with 12 pentagon faces, can be distorted so that it can be drawn with no lines crossing.  In fact any convex polyhedron has this property (loosely ‘convex’ means no dents or spikes). Related is the fact that for convex polyhedra the number of vertices, minus the number of edges, plus the number of faces is always 2. Here that is 20 red vertices - 30 edges + 12 faces = 2. Can you draw a cube with no lines crossing, and does the formula work add up to 2? [more] [code]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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