Not sure I understand "The idea is to use the less parts as possible. "
I only have two different parts in the diamond frame - long edge and short edge. And all ten diamonds are identical. The joins between them in my suggestion are simple butt joints, easy to make and join together.
Are all your parts identical?
If you bevel the edges so that adjacent diamonds meet closely both in and out-side their thickness, I think you will need matching Left and Right pairs of sides - that’s also two different parts, which I think will be much harder to cut with that sharp pointed double tapered end, and more fragile to join.
On reflection, I think the bevel angle must be exactly 18 degrees, not as I have shown it variously as 18.1 or 18.2 degrees - you can fit a pentagon inside the diamonds, so the bevel angle is, I think, one quarter of 72 degrees.
Anyway, best of luck with further drawing, and eventual construction.
BOX, after a closed look at your diamond spheres, i saw that you didn’t use square 1 x 2" planks.
The top of the joints are flat and they should be.
Again, thank you for your inspirational work.
BOX, since some angles from your Diamond Sphere was not corresponding to my geometry, I took a closer look.
I exploded a diamond and made a cross section of one of the timber…
They are not square !!!
I did say it was a quick pub doodle. You only need to adjust one component to correct the error.
I don’t really have the time to go further with this just now, but here is a corrected one. Diamond to correct size.skp (56.1 KB)
FYI fine Wood Wood Working #158 Sept/ Oct 2002 has article from North Bennet Street School in Boston : " Compound Angles Without Math" My younger daughter wanted serving try with the 4 sides flared out and used this approach to cut their compound joints and assemble without any mechanical attachment except hide glue. I have a machinist protractor and the few arc minutes still make joints that don’t fit some times.
Sorry it is copyrighted so cannot copy.
