Shopsmith Forums

]Thanks for the challenge. Now that I can draw it maybe I can make it.

Ahhh - so it be a solid, not any of that other stuff?

Impressive. I can't imagine how to go about making one.

BTW, a pyramid has four faces, but it isn't a "regular" tetrahedron, because its base is a square, not a triangle.

john_001 wrote: ↑Thu May 04, 2023 4:53 pm BTW, a pyramid has four faces, but it isn't a "regular" tetrahedron, because its base is a square, not a triangle.

I know what you're trying to say. However, a pyramid with a square base is not any kind of tetrahedron because it has five sides, making it a pentahedron.

And it is extremely impressive work.

JPG wrote: ↑Wed May 03, 2023 6:54 pm Ahhh - so it be a solid, not any of that other stuff?

It be a solid if you make it that way but that is not what I intended.
Whatever is wanted:

Aha! Sometimes the old ways are the best ways! Thanks for the photo of your set up. Now I just have to figure out how to do the layout of those shapes... Very cool Moxon vise, by the way.

Just to be clear a pyramid can have a square base, a triangular base, circular base or any other polygonal or otherwise shaped base. Triangular based pyramids are common, though I guess when I said I saw pyramids intersecting in the earlier picture, some may have assumed I meant a square based pyramid like an Egyptian pyramid as an example. That was NOT what I meant. FYI...a triangular based pyramid is ALSO known as a tetrahedron, but a tetrahedron is a special type of triangular based pyramid in which all edges are of equal length and all angles are equal, so it is a subset. IF Glenn's construction on this thread has equal angles and equal length edges (before merge of course), then it qualifies as a tetrahedron. Otherwise, it is the merging of two triangular based pyramids.

I'm running out of scrap wood (aka, cutoffs) trying to figure out how to cut one of these.

edma194 wrote: ↑Thu May 04, 2023 5:45 pm

john_001 wrote: ↑Thu May 04, 2023 4:53 pm BTW, a pyramid has four faces, but it isn't a "regular" tetrahedron, because its base is a square, not a triangle.

I know what you're trying to say. However, a pyramid with a square base is not any kind of tetrahedron because it has five sides, making it a pentahedron.

And it is extremely impressive work.

Oops,sorry - miscounted.

I have half of one of these emerging from a block of pine. It's rough, I started with some unnecessary cuts, you can see that on the bottom corners. It's only material that would get removed later from other cuts, but it helped me solidify the concept in my head. Glenn provided enough hints on how to make this. If I make another one I'll take pix of each step. It's not that difficult, if I can work out the compound angles it should be workable on the bandsaw. If you do this with a handsaw make sure you have a good sharp one. Wish I had one right now. Some useful info about this shape: Glenn already pointed out that it can circumscribed by a cube. There's also a square formed by the points where the two tetrhedra intersect.