in Lightburn how I can determine the thickness of a slot when you have 4 pieces intersecting in on same axis

This is sort of what i want to design trying to find the width of the 4 slot for each pieces intersecting in this pumpkin. it is for something similar to this.

You write 4 parts, in this case it is easy. 2 wings which can be stuck together in the middle with 2 opposite notches which are as wide as the thickness of the material. But the picture shows several parts, it requires a different construction.

Okay, so what you’re looking for is four pieces that all slot together, which would look like this from above (if they could pass through each other), yes?

So, then, each piece would have 1/4 of the slot connected so you could stack them, basically like this?

In that case, we just have to break out a little math. Zooming in on the center crossing…

Let’s call the thickness of the stock material X.

The full vertical red line, then is the diagonal of a right triangle with sides X, which makes it X√2.

That means that the darker red portion is half of the extra length, i.e. ((X√2) - X) / 2.

The blue line, then is twice that, or ((X√2) - X).

Since the green triangle is also a right triangle with 45° corners and the vertical green line is X, the horizontal green line is also X.

Putting this all together, the magenta line, which is the required size to have a non-interfering slot, is 2X + ((X√2) - X).

Simplifying, that makes it X(1 + √2), which is about 2.414 * X.

So, a non-interfering slot would be about 2.4 times the thickness of the material, but you’ll certainly want to adjust that slightly for kerf, et cetera, so you get a nice fit. If you’re making it out of a somewhat compliant material, e.g. wood, you can probably go a bit tighter than if you were using something like acrylic, and if you hit the edges of the slots with a quick sanding, that will also let you tighten things up a bit.

Of course, this is just me slinging some math. I’d love to hear the final parameters someone ends up using and compare them to the purely theoretical.

Mathematically and sanding only one side of the slots should work, but if we have to make a groove in the flat faces where the slot rests, I think it will be weak.
I didn´t done any intersecting like this but I believe it´s better a glued loose fit, of course I may be wrong (only testing).