# Laser-cut Press-fit Construction Kit

## Step 0: Pick something to make

Let's laser cut a soccer ball.

## Step 1: Parametric Polygons

Soccer balls are technically truncated icosahedrons and are one of only thirteen "convex isogonal nonprismatic solids whose faces are two or more types of regular polygons". Soccer balls have both hexagonal and pentagonal sides, so I wanted a parametric sketch that could be an arbitrary number of sides. You can't do this in Fusion with the actual polygon sketch shape; you have to make your own with the rotate tool and careful trigonometry.

"Premature optimization is the root of all evil."
This seemed like a good idea for a while, but after an hour of congratulating myself on how great an idea this was without making any progress, I just gave up and made a parametric pentagon and a parametric hexagon separately and set their side lengths to the same variable. `¯\_(ツ)_/¯`

## Step 2: Joint Testing

Even lasers have width, so the peaks of the edges have to be wider than the valleys.
This meant for a polygon with `n`

sides and sides lengths `l`

, each peak had to be `(l / n) + 𝛿`

and each valley `(l / n) - 𝛿`

for some `𝛿`

.

After a few trials, I settled on `𝛿 = 0.4mm`

. Each seam overlaps by `2𝛿`

so there's `0.8mm`

overlap for every joint.

## Step 3: Cut with Laser

A truncated icosahedron has 20 hexagons and 12 pentagons, which just about covered an entire 24x36in sheet. I filled the remaining space with extras, just in case some didn't pop out

Two passes with the laser cutter took 20 minutes each. For some reason the bottom left quadrant of the sheet didn't cut through the bottom layer of the cardboard at all- I ended up with just enough pieces without it.

## Step 4: Assemble with Hands

Assembling the ball was an adventure all on its own.
The very beginning was easy - the joints felt secure and held together well.
The *middle* - the ring of hexagons halfway up - was terrifyingly unstable, and I was certain I wouldn't make it without the whole ball collapsing.
But once I got past the middle ring and started enclosing the ball with the upper pieces it became dramatically more secure.
The finished product is solid enough to drop or throw around. For now it's hanging from my ceiling.