I am working on a design for a hardwood door that would feature square, pyramidal panels. In masonry such shapes are called "diamonds". The question is how to shape the panels and do the joinery into the structural members of the door. I have shown the section and elevation below with approximate measurements:
Trying to cut the panels out of a single slab of 2" board has challenges, but on the other hand trying to make them in pieces also has complexities.
The traditional way to do this, is to have the central diamond be on piece of wood, and the raised portions around the edge be a separate frame. The frame is held together with mortise and tenon joints, and has a groove into which the central panel fits. The central panel is not glued in place, to allow for expansion.
Normally, the central panel is a constant thickness over most of it's width - it's just the edges that are cut back. You can do this with a spindle moulder. For this design though, I think you would want a spindle-moulder to do the edges, and then mount the piece in a jig, and feed it through a planer-thicknesser. You'll have to feed it through once for each plane of the diamond - so eight times in all. Getting the jig right is going to be fiddly!
One option if you don't mind a little math, careful blade height adjustments, and using a hand plane:
Calculate the depth at a series of distances from the center of the pyramid, say every quarter inch. Set a table saw blade height (carefully) to that depth and cut concentric squares around the pyramid at each corresponding depth. Make sure the inside of the kerf (from the center) is aligned to the calculated position.
Then, using a shoulder plane, remove the remaining ridges to the point where the cuts disappear and then flatten the angled surface.
This is a bit of work but with a nice sharp plane it will go faster that you might imagine. A second plane with a more aggressive setting could help with removing the bulk. One problem here will be going across the grain on two of the sides depending on the species of wood.
The diamond piece could be cut with a router planing jig - basically, a pair of rails that sit on your work table, along with a sled that your router is mounted to. The sled rides on the rails, which allows the cutter to move along a 2-D plane a fixed height above the work table. It's almost like an upside-down router table, in the sense that your workpiece is fixed and your router is moving in relationship to it with the relationship defined by the rails. There are many examples available on google or youtube if you're unfamiliar - starting to use router planing jigs a few years ago has really changed the way I do many woodworking operations for shaped panels like this.
Your workpiece would be clamped between the rails, with a shim underneath one edge to raise that edge up off the work surface and set the angle at which you want to cut the facets. The shim could be screwed or clamped to the work table in a fixed position, which would allow you to turn the workpiece through 90 degrees and clamp it back down to cut each of the 4 facets. Then, double the height of the shim, flip the piece over, and cut the 4 facets on the opposite side.
