Soccer Ball, Or Truncated Icosahedron

[Fabrickator]

Once again, I was looking for a challenging project and I certainly found one. I like to call it the “Death Star” because the flat-sided form looks like something out of Star Wars, nevertheless all of the difficulties I had trying to unlock the mysteries of the math. Look closely at a soccer ball and you will find that it is made of both pentagons and hexagons, in divisions of five.

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

 

[ch2co]

Rick
Beautiful work as usual.
What do you use to verify that your angle plate is at the correct angle? I would think that with that many facets, even a slight
error in the plates tilt would prove to be quite visible.

CHuck the grumpy old guy

 

[Fabrickator]

Yeah, one little mistake and your done. I use one of those little mag base digital protractors (Fowler) I bought from Enco. Even still, it's not that easy to dial in. I use my Starrett bubble level on the Diamonds are Forever project, which was even harder. When I made the angle plate I made it really stout out of 1/2" plate and I'm glad I did if you noticed the long overhang at the lower angles.

I finished it with a quick polish tonight, I'll post the pics tomorrow.

 

[Fabrickator]

Here are some pics of my method for finishing a ball. I polish what I can before losing the both tenons. Part off, finish sizing one end, and polish it while I still have one tenon left. Epoxy the ball into my cup fixture I made for the "Diamond" project using the live center for perfect alignment. Part off and finish size the last end, and polish it out. Hope you like it.

Rick

 

[brino]

Another stunning result. You certainly do like a challenge, and even more certainly rise to that challenge.

What kind of polishing wheel is that? Just cotton? What polishing compound do you use? I have never achieved that mirror finish on aluminum.

Thanks for sharing!
-brino

 

[Fabrickator]

Thanks Brino. I'm always looking for a challenge and this was probably the hardest yet as far as cracking the code. For now, I'm finding 3-D geometric shapes are very intriguing. I designed my own 4-stroke, twin cam engine but I'm saving it for when I retire in a couple of years.

I use what were about 10" "soft" cotton wheel(s). One set for tripoli, one for white diamond, and one for carnuba wax compounds. I also got three ball-type buffers for inside work when I purchased them I originally bought them for my woodworking (vase & bowl projects). Your starting finish is very important to minimize polish time. It's especially important when your dealing with crisp edges that you don't want to roll off. The Superbowl football was super easy, as opposed to how careful you need to be with something like the soccer ball or diamond projects. I start with tripoli until is basically done. Then I follow-up with the white diamond for another lever of bright. I only use Carnuba Wax to put a moisture proof finish on wood projects.

 

[brino]

For now, I'm finding 3-D geometric shapes are very intriguing.

Soon enough you'll be off to 4 or more dimensions......

Thanks for the responses.
-brino

 

[Steve Shannon]

That is very neat. For jewelry we used to finish with rouge for the shiniest finish. I used a ton of tripoli but I never used white diamond (don't even know what it is) so I can't compare. Rouge was cheap and worked well.


Steve Shannon

 

[Fabrickator]

It comes in a 4" bar like tripoli, but is white . I think it's just a finer grade (like a rouge). I use it with very little pressure for a final polish. Tripoli works the metal pretty aggressively and generates a lot of heat to actually move metal.