Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?

01312019, 06:07 PM
(This post was last modified: 01312019 06:15 PM by StephenG1CMZ.)
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Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?
Over on quora I just saw an interesting question: What is the opposite of a sphere?
My nontechnical guess was all the space outside the sphere (like a torus but in 3D). That has the advantage of being easily visualisable in 3D. But what is the defining characteristic of a sphere that we want the opposite of? Some answers suggested a negative curvature, and that sounds mathematically interesting, but I'm not yet visualising how that looks. Other answers picked on the number of corners, but I don't think it has a definite number. It seems to me you can make a case for both zero and infinity. Another answer suggested that a sphere minimises suface area/volume, so its opposite should instead maximise that ratio...But what shape has that characteristic? Stephen Lewkowicz (G1CMZ) 

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