Monday, January 30, 2012

Rhombic Triacontahedron Fabrication

A rhombic triacontahedron is a 30 sided polyhedron.

Each face is identical. It's made by taking a golden rectangle and connecting the midpoints of each edge which results in a diamond shape:

Here's the one I made from 1/2" thick walnut and ash. It's about the size of a volleyball.

It’s actually held together with magnets – 120 of them – one in each edge.

It was cut on a 5-axis CNC at the Taubman College at the University of Michigan. Here’s the machine and the fixture which holds the work as it’s cut.

Vacuum pressure comes through the table and fixture to hold it in place. Two tiny pins prevent it from twisting during the cutting and drilling.


  1. Hi Mark, I've been looking at your blog a fair bit in the last two days and I really admire your innovative solutions to the complex fabrication of these projects. Of particular note are your work-piece holding set ups, the example here is great it really helps me to open up some more possibilities to have custom shaped vacuum hold-downs, and the pins are a great idea. I couldn't help but notice though, that you could have reversed your tool paths to cut the diamonds from the outside in, so that your pin marks would be on the inside of your triacontahedron. I believe a downward spiral cutter would have made sure that the finish was acceptable in that case?

    1. Hi Ryan, Getting the pin marks on the inside would have been nice. One issue is I had the drill the holes for the magnets. That had to occur from the top. Also, I think I was right at the limit of a size that would work at all. Several pieces came loose and went flying during the cut as is.
      If you invert the piece on the fixture, the surface area is even smaller. Further, think about the tool - it would be cutting beneath the part. Which is okay, but you'd need to move the rubber gasket in even farther so it isn't cut into by the tool. So the area for vacuum pressure would be REALLY small. You are right, a downshear would have kept the tear out down. If the ball was twice as big, I think that solution would have worked and been better, although again it would necessitate a flip of the part on the fixture for drilling.