Well... I'm not actually turning a pyramid as such, but I'll be needing to mount my blank along the same 4 axis as a 3-sided pyramid, a tetrahedron. ie. 120° offset to each other.

My problem is that I'm trying to mark them out on a rough cube. Well... the blank's actually a more organic shape but I've roughed it to approximately cubical in an attempt to make marking easier. I suspect that even if I machined the blank to a perfect cube, finding the required centres wouldn't be any easier.

I'm currently considering turning the blank spherical, which'd make laying out the lines much, much easierr; a case of simply marking out 3 circles offset by 60° intersecting a common point then divide each circle in 3 to give me the circumference of the 4th.

Unfortunately, that'd reduce the size of the finished item too much, as I'd also need to make allowances for (and remove) tenons for mounting.

Suggestions?