# Dome-shaped jigsaw puzzle

There are a lot of wonderful Glowforge-made polyhedra out there … also a lot of cool puzzle globes.

So I wanted to do something a little different, essentially a 2-D jigsaw puzzle in the shape of a dome. My goals were:

• No internal supports
• No special connectors, just traditional puzzle pieces with knobs and sockets
• Random irregular polygonal pieces (not a regular polyhedron)
• A seamless surface

This one is 1/16" thick and 15" wide, 498 pieces.

There are hints (polar coordinates) scored on the backs of the pieces.

The pieces are close-fitting even though they meet at an angle. For once, the V-shape of the kerf is an advantage. As long as the pieces are cut upside-down, and the angle between the pieces is shallow enough (it’s around 6°), the V-shape allows the top edges of the pieces to remain touching.

The edges of adjacent pieces were designed to meet exactly. And they do — or at least they can. In practice, getting all of them perfectly level simultaneously is super difficult. When you handle the puzzle, the whole thing flexes and the pieces start shifting.

Assembling the puzzle is tricky with only two hands (but it can be done). It takes some care to keep it from falling apart during handling. Flexible fragments won’t fit together if they’re not at the right curvature.

But when assembled, it has surprising load-bearing capacity. Here’s a 21-pound stack of textbooks sitting on it — no internal supports, and it’s only 1/16" thick!

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That is fantastic. Well done.

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Well, that is super cool! I can only imagine how difficult that would be to piece together. Holding all that weight is amazing.

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That is impressive both shape and strength

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Obviously, the shapes weren’t designed by hand. I wrote a bunch of code.

The first step was to generate a random, deliberately irregular, approximately-spherical polyhedron. I used a simulated annealing algorithm to get a set of not-quite-evenly-spaced points on the sphere. The intersections of the points’ tangent planes became the sides of the polygonal faces. (The projection of this onto the sphere is actually a spherical Voronoi diagram.)

Note that the V-shape of the kerf doesn’t control the curvature of the sphere (more accurately, the irregular polyhedron). The geometry is determined by the angles at the vertices (see Wikipedia:Angular Defect).

For the picture, I started with this (flat) AI-generated image:

Treating it like a top-down view (orthographic projection) of a hemisphere, I then computed the images for the pieces, using a separate gnonomic map projection for each piece.

I laid out the pieces separately (it took 8 letter-sized sheets) and cut them with a kerf adjustment. The scored hints on the back were automatically computed, and I used the digits from the Hershey font.

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Whoa – that’s super!

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Amazing!

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Goodness! That’s incredible!

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I don’t even understand 50% of your description, but I can appreciate your skill! The strength of domes I knew about

So cool!!

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Wow! I have to say I am bowled over.

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Adding my voice to the choir of Wows. This is so unique and so much work - and it worked! Thank you for sharing how you did this - even if I don’t comprehend a lot of it. An artistic, engineering feat.

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Incredible, Amazing and Beautiful.

You have been chosen as a Glowforge Superhero.

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That’s just a whole lotta WOW!

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OK my mind is blown, now I gotta clean all the gray matter off my desk before the hospital infection control people see it!

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I also only understood bits of your write-up! This is such a cool puzzle!!! I love it!

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That’s what you get for reading the forum at work

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All I can say is a big giant “WOW”. That is fantastic.

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Understanding it all is way over my head…but appreciating your skills, knowledge, and the beauty of your puzzle is not.

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That is a work of art in several ways.

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An incredible job of bowling indeed!

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