...another point of clarification... for cone #2, I described it above as a 'flat' mapping, but what I actually used is called a 'shrink' projection in BodyPaint, which instead of just a stright-on (from above) projection, it also tries to compensate for polygon area coverage, so you end up in this case with the sides being mapped something like the spokes of a wagon-wheel (selected, in the attached image).

The point of that cone and mapping style is that there are no seams - around the circumference of the cylinder/cone.

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