- Joined
- Jan 22, 2014

- Messages
- 577

Here is the formula from Wiki:

Or, if you prefer the long form equation see the pic.

Anyway, the geometric shape dates back to Archimedes (212 BC), Leonardo De Vinci (1500) and many other great mathematicians. It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

Once you crack the measurement code then there are the mechanical and procedural problems. There is the problem of mounting it to cut the facets on one end and then flipping it around and get it perfectly indexed to cut the facets on the other end. If any of these factors are off by just a bit, it won’t work. If you screw up one “side” of a pentagon or hexagon, it will plague you throughout will never work out, much like a geodesic dome structure.

Since this was my prototype, I made it out of a 2 ¼” piece of 6061 aluminum bar stock I had around and it ended up just under 2” diameter. All I have to do now is the easy part. Cut off the ends, finish sizing and polish it. I'll post the finished pics once it's done.

I’ve since bought a 3 ½” piece of acrylic rod stock to make a “crystal ball” version. This project was all done freehand with no auto-feed or CNC.

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Equipment:

Grizzly G0602 w/ball cutting fixture

LMS Mini-Mill w/DROs

Angle Plate Fixture w/rotary table & collet adapter

1 ½” End Mill

Rick