To be clear, this is presuming a (multidimensional) bell curve distribution for dart throws, or weights and heights, or for whatever. Let us be clear that the G

To be clear, this is presuming a (multidimensional) bell curve distribution for dart throws, or weights and heights, or for whatever. Let us be clear that the GCI is specifically about bell curve (i.e., normal, Gaussian, etc.) distributions, not about anything else. Also, I believe the shapes must be not only convex, but symmetric under reflection through the center. But it suffices to consider only parallelepipeds.