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enter image description hereWhat are the correct formulas for calculating the area and the volume of the gömböc, if any have developed them? If there are none, could you help creating them?

The gömböc is a neat convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium that corrects itself if tipped over. (From Wikipedia).

"Reference": https://en.wikipedia.org/wiki/Gömböc

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    $\begingroup$ @peterheinig: it is in fact not unique up to homothety. $\endgroup$
    – Steven Landsburg
    Mar 1, 2018 at 13:25
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    $\begingroup$ Importantly, of course, the plural is gömböcök. ;) $\endgroup$
    – Billy
    Mar 1, 2018 at 15:17
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    $\begingroup$ The origin of the words is Greek, not French. $\endgroup$
    – Emil Jeřábek
    Mar 2, 2018 at 10:35
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    $\begingroup$ Analogy is definitely not a valid principle in linguistics. $\endgroup$
    – Pietro Majer
    Mar 2, 2018 at 14:18
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    $\begingroup$ As mentioned above, there is not a unique gömböc up to orientation and scaling so the question asked in the body about the volume and area of "the" gömböc is underspecified. You might try to improve the question by specifying one particular gömböc that you're interested in, but then, as you probably know, the area and volume of any solid body can be computed by integration, rarely have closed form evaluations, so I doubt that you will find formulas better than these en.wikipedia.org/wiki/Volume_element $\endgroup$
    – j.c.
    Mar 5, 2018 at 0:51

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