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!
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.
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.
