# Lighting Pendants #1: Truncated Icosahedron challenge.

 Blog entry by MarkTheFiddler posted 06-24-2014 06:37 AM 1244 reads 2 times favorited 18 comments
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Howdy,

I’m making two chandeliers for the living room. I don’t know why I thought it might be a good idea to hang soccer balls from the ceiling. I just got it in my head that they would look good up there. Now I’m all in.

The top half of the chandeliers will be solid wood while the bottom halves will be made from the wooden cages.

Since I’m posting this from my I-phone, the pictures might turn out sideways or upside down. ;)

This is two top halves resting on top of each other.

And a few more images of the dry fits.

I still have some cutting to do but the dry fits are promising (not perfect).

I tried looking around the LJ site for information and found a few helpful pointers. I found a few different values for angles so I had to do a little research to find out which ones were correct. I’ll give the best details I can right here.

There are 12 pentagons and 20 hexagons in each ball. Each pentagon is surrounded by 5 hexagons. Each hexagon is surrounded by alternating hexagons and pentagons.The outer angles are set at 60 degrees for a solid face. The outer angles on a solid face pentagon are 72 degrees. That’s the easy part. By the way, I’ll get to the cage angles in the next blog.

Now for the hard-ish part. Each shape has an angle on the where each side connects. Those are called the vertices. Wikipedia doesn’t tell what those angles are but it gives the next best thing. Those are the outer angles. They are a little different from hex to hex vs. hex to pentagon. Lets start with hex to hex. The outer angle is 138.189685. Whew! The inner angle will be that figure subtracted from 180 degrees. That gives you 41.810315 degrees. If you divide that in half. You get the angle of your cut which is equal to 20.9051575.

My wixey angle only reports 1/10th of a degree measurements. For all practical purposes, the angle for hex to hex cuts is 20.9 degrees.

The pentagon to hex angles are slightly hard-ish-er. For starters, the outer angle is 142.62. That makes the inner angle 37.38. Here is the stumbling block. If you cut all of the hex sides down to 20.9 degrees, then you need consider that when cutting the angles on the pentagon. Your pentagon cuts will be 16.48 degrees. My wixey allows me to cut at 16.5 degrees.

Joining the two angles when the wood is the exact same thickness will cause the side with the greater angle to appear thicker at the but joint. If you want avoid that you can cut the pentagon to 18.69 (18.7) degrees but every other angle on the hexagon must be cut to match. Talk about a lot of preplanning. You’ll have to know what the grain direction for every hexagon will be before cutting every other angle. One at
20.9 and the next at 18.7. That’s too much room for error for me.

Last bit of information. I don’t have the precise figures here but each edge of my polygon is 2 and 3/4 inches wide. The ball has a diameter of about 13 inches.

Best of luck to you. I’ll post more when I get there.

-- Thanks for all the lessons!