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Adrian,

Nice job finding the equation to calculate the centroid of the Chestahedron. The vast majority of polytopes require an algorithm to find the centroid, but for special cases of symmetry, this aspect can be used to intuite a formula.

Oh, and thx for clarifying the distinction of the volume centroid versus the vertex centroid. Now, I have to go off and find out exactly what that means (beyond the formal defintion, that is)...

Wow, Guy! Great stuff. Thx. Much of what you shared I have been discovering along the way, or at least getting a hint of. Thx for so eloquently clarifying things. A fascinating journey it has been:)

As for the Chestahedron and the midellipsoid I discovered for it - yes, I got "lucky":) And, as noted in last reply, I'm curious to see what might come from using it as the surface of reciprocation.

Also, looking forward to checking into the 'Vertex Figures' link, plus your polys page! Thx.