Lighting Pendants #1: Truncated Icosahedron challenge.

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Blog entry by MarkTheFiddler posted 06-24-2014 06:37 AM 2633 reads 2 times favorited 18 comments Add to Favorites Watch
no previous part Part 1 of Lighting Pendants series Part 2: Oops, Eureka, Cool! »


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!

18 comments so far

View GrandpaLen's profile


1650 posts in 2268 days

#1 posted 06-24-2014 11:01 AM

”The pentagon to hex angles are slightly hard-ish-er.”

...omg Mark, SERIOUSLY??!!!

If your brain doesn’t feel like it’s been massaged with a cheese grater by the time you finish this, what then will be your next project?

Best of Luck with this one :-)
Work Safely and have Fun. – Len

-- Mother Nature should be proud of what you've done with her tree. - Len ...just north of a stone's throw from the oHIo, river that is, in So. Indiana.

View HillbillyShooter's profile


5811 posts in 2288 days

#2 posted 06-24-2014 12:11 PM

“I don’t know where to go with that . . .” My brain hurts after reading your post, let alone trying to really process the geometry and math. ;-). All I can say is you’re way over my head, but my best wishes to you on this project—you’re obviously having fun.

-- John C. -- "Firearms are second only to the Constitution in importance; they are the peoples' liberty's teeth." George Washington

View kirbi69's profile


83 posts in 1580 days

#3 posted 06-24-2014 12:21 PM


View MarkTheFiddler's profile


2068 posts in 2184 days

#4 posted 06-24-2014 01:02 PM


Yep – I’m having fun. I’m nerding up a storm too. This stuff has me fascinated. When you see me post those long scientific words like hard-ish-er, you can probably bet that I forgot my pills.

I’ll try to explain it a little more simply without the silly brain dump.

Take a look at the following hexagon. It’s bigger on top than at the bottom. The angle of that cut is 20.9 degrees.

This pentagon was cut to 16.5 degrees (16.48 if you can swing it).

Better? By the way. I used other LJ projects as my guide. Thanks to all for laying the groundwork!

-- Thanks for all the lessons!

View GrandpaLen's profile


1650 posts in 2268 days

#5 posted 06-24-2014 01:29 PM

Mark, if you had been the ‘on site supervisor’ 6314 years ago, would we today be in awe of
‘The Great Domes of Giza’ ?? ;-)

Sorry I can’t help myself.

Not to take anything away from the soccer balls that have been featured on our site in the past, which to me are pretty intimidating, your challenges in woodworking are amazing!

I will be following your Blog with much anticipation as always, but for this ‘Old Dog’ a good looking 45 degree miter joint in my shop at the end of the day is quite pleasing. ...just sayin’.

Best Regards. – Len
Work Safely and have Fun.

-- Mother Nature should be proud of what you've done with her tree. - Len ...just north of a stone's throw from the oHIo, river that is, in So. Indiana.

View kiefer's profile


5619 posts in 2663 days

#6 posted 06-25-2014 12:27 AM

Mark I wish you all the luck with this one and will wait for the finished project .
All those angle settings are very confusing but fascinating .

-- Kiefer

View waho6o9's profile (online now)


8189 posts in 2573 days

#7 posted 06-25-2014 03:15 AM

I always wanted to make those, a definite favorite

and good luck Mark you’ll do great.

View MarkTheFiddler's profile


2068 posts in 2184 days

#8 posted 06-25-2014 05:54 AM

Keifer and Waho, thanks for the well wishes guys. I’m definately in over my head. By the same token, men have landed on the moon. That was before we had a clue about how many things could go wrong.
I did a similar project before. That’s before I had a clue about how exacting everything needed to be. I’ll find out soon if this project is worth or it turns into something I wish I hadn’t started. ;)

-- Thanks for all the lessons!

View stefang's profile


15881 posts in 3330 days

#9 posted 06-25-2014 08:15 AM

This looks like an interesting and challenging project Mark and the fit looks pretty darn good. I think you could get a perfect fit with a sanding jig similar to the kind used for segmented wood turning. If set up correctly one could deliver perfectly sized and tapered pieces. Just a thought.

-- Mike, an American living in Norway.

View MarkTheFiddler's profile


2068 posts in 2184 days

#10 posted 06-25-2014 12:43 PM

Mike, I can definitely see how that would help. The only sanders I have are a 5 inch orbital and a belt sander. I’ll have to think hard about building a jig. Thanks for the advice!

-- Thanks for all the lessons!

View MarkTheFiddler's profile


2068 posts in 2184 days

#11 posted 06-26-2014 04:38 AM


I’m taking my time on the build. The first time I built one like this, I tried to glue everything up at once. It was just a dodecahedron, but there were plenty of parts to mess up. The clamps couldn’t hold it together while I tried to get the next piece attached. There was lots of sliding and the whole dawg gone thing fell completely apart a few times.

I hope I’m not heading for a crash but I do do know that what I have so far won’t come apart at the seams. However, there’s something to be said for a little glue joint slippage when you pieces are not precisely cut. I’ll find out tomorrow how badly I messed up or how good I did.

Here is a clamping trick that seems to be working. I use sturdy box tape to secure an outside edge. I fold open the joint and careful apply glue to minimize squeeze out.after that, I fold the joint up the apply tape across the two pieces of the inner angle to close the seam. The joint are holding very well.

-- Thanks for all the lessons!

View lightweightladylefty's profile


3238 posts in 3708 days

#12 posted 06-26-2014 06:03 AM


Not in my lifetime! This is way beyond any precision I could achieve. I once tried to make a cube with all sides mitered and I couldn’t get the 45s and 90s accurate enough to make it look good. No way could I come close with what you’re doing!


-- Jesus is the ONLY reason for ANY season.

View MarkTheFiddler's profile


2068 posts in 2184 days

#13 posted 06-26-2014 12:44 PM

L/W, I’m not buying it. You made all those wonderful box joints for your cabinet drawers. You have incredible patience. I say, go try that mitered box again. You’ll be surprised at how crisp and clean the edges turn out. The rest of us already know it will be perfect.

-- Thanks for all the lessons!

View Joe Lyddon's profile

Joe Lyddon

10096 posts in 4048 days

#14 posted 06-26-2014 10:29 PM

COOL stuff!

-- Have Fun! Joe Lyddon - Alta Loma, CA USA - Home: ... My Small Gallery:"

View MarkTheFiddler's profile


2068 posts in 2184 days

#15 posted 06-27-2014 01:18 PM

Thank you Joe!

Yesterday morning, I tried dry fit a pentagon into one of the fixtures. It doesn’t fit. I then tried two more hexagons, that was a very nice fit! I rolled the dice and glued up 2 side by side hexagons onto the fixture. Very nice!

The pentagons got skewed a little when the saw grabbed them during cutting. The Paduak pieces are very slightly skewed. The Purple Heart – a little more. To make the pentagons fit, I’m going to finally invest in a bench top sander and just marginally remove tiny bits of material until the pentagons are seated perfectly. Thanks Mike!

-- Thanks for all the lessons!

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