Most Irregular with Ben Craven

I love the way new ideas can spring from conversations , how one project can be the spring board for a new one. Here are a few words from Ben Craven about how Illuminating Geometry gave him a new idea that has kept him busy for months!

Ben's irregular polyhedron.

Ben’s irregular polyhedron.

One day last year I spent a few hours talking to Jenny about the Platonic solids that she’s been working with, and it made me wonder: what do irregular solids look like? Would they be ugly, beautiful, disturbing, interesting, boring, or what?  And how would you set about making them?


The thought nagged away at me, until eventually over the Christmas break I sat down and started writing computer code to generate irregular polyhedra. The starting point is a sphere: each face of the polyhedron is part of a plane tangent to the sphere. All of these planes intersect each other, and the lines of intersection form the edges of the polyhedron (and hence the boundaries of the faces).


By varying how the tangent points of the planes are distributed over the sphere, and also by having each face tangent to a sphere of slightly different radius, I can vary how irregular each polyhedron is. I don’t place the faces by hand – I set up a process and see what it comes up with.


Here are pictures of a 10-hedron made out of card, and an 83-hedron made out of thin layout paper. (Yes, the 83-hedron was difficult to glue together, and yes, it did take many hours!)  They have quite different characters: the 10-hedron feels like a wonky polyhedron, but the 83-hedron is well on the way to looking like an irregularly tiled sphere.


I rather like them, which is just as well given how much time they’ve taken.  What about you?


Ben Craven

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