I've only made two pyramid shaped range hoods in my short cabinetmaking career. The one I'm working on now is four sided and will be above an island. I had a friend make a program in Excel that would spit out the correct compound angles most of the time. At times, though, the angles seem to be off. How do you figure out the tricky angles? Trial and error method seems to be too time consuming, especially because I do custom work and each job is different. That's a lot of test fitting.
(Cabinet and Millwork Installation Forum)
From contributor J:
Why not try a scale model? Say a size you could cut on your compound mitersaw. That will give you your angles.
If this is what you are talking about, then contributor J gave you some very valuable info. Build a scale model first. That will give you your angles. Construction of these hoods isn't difficult at all.