cityrail ticket cubohemioctahedron

cityrail ticket cubohemioctahedron

A while ago, as many of you would, I saw the Metrocard tricontahedron linked from the Makezine blog.

This weekend, whilst hacking away, I took a break and was distracted by the large pile of used tickets that have built up on my desk. I found the above site again, and spend about 15 minutes folding some tickets until I emerged to the loungeroom to show off the results.

cityrail ticket
cubohemioctahedron (flickr)

So what it this shape actually called? I googled ‘tricontrahedron’ (because I can’t read) and then ‘tricontahedron’, and discovered that this name is derived from the prefix tri-, the modifier conta- (which refers to a group of ten), and the suffix -hedron, meaning “faces”, so we have a 30-faced polyhedra. True so far, but actually googling or searching Mathworld for tricontahedron wasn’t showing me any graphical evidence that this was the right name. In fact, the closest by name, the rhombic tricontahedron, looks nothing like this shape.

But finally I stumbled on a set of excellent polyhedra sites:

Thanks to FreeWRL I managed to finally find the cubohemioctahedron, which although the image on that linked page doesn’t look terribly much like our shape, upon loading the VRML for the polyhedron I was able to convince myself that this is the one.