Badger also mentioned keeping width parallel out of the fades for 2-3" and I have used that as well. It does a great job of evening the stresses out right at the end of the fade into the working limb portion. There tends to be a bit of a stress concentration right at that point and a short parallel section smooths that out.
A second thing not mentioned yet is that the theoretical pyramid shape tapers to a sharp point at the nocks. Since this is impossible in reality the way around it is to layout the pyramid taper to a sharp point, then draw a short parallel width lever section from the nock to where it intercepts the pyramid taper. This can be as narrow as you think you can make it. On my last lam bow I think that lever is about 5/16" wide for something like 6". I was worried about that being fragile and maybe unstable but it has not proven to be so.
If you straight taper to the nocks with some width at the nock then it tends to overstress the middle of the limb a bit and you need to taper the thickness in the outer half of the limbs to balance that off.
Mark
You are hinting at something here but didn't explain all the way through. The perfect pyramid tiller looks like a circle. But we can't build a perfect pyramid for the reasons you described. So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.
Since a pyramid bow is essentially a piked bow, you know that the tiller shifts when you pike the bow. The tips gain more leverage and get stiffer, which pushes the stress towards the inner limbs. You need longer parallels than what you said was suggested. You need about 7 inches per my experiences, as a little loss in length magnifies in stress as the distance increases. 7 inches is a rough number. There is a ratio to explore but I don't know it yet.
In short, it's my strong opinion a pyramid bow shouldn't actually be a pyramid, nor tillered like one. It should start out parallel, then straight taper to stiff tips. Tiller should be stiff tips, that lead to an ellipse. That will allow the short coming of what is possible to be compensated for vs what works on paper.
All that said, a well made pyramid bow will not fail you as Old Self bowman aka Arvin has proven time and time again.
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