Le_Forgeron <jgr### [at] freefr> wrote:
> More than the classical cone/sphere/cylinder used to count 1,2,3.
>
> Counting from 1 to 6, here a set of increasing volumes.
> Constraint are:
>  * Volume must be inside a box of size 2R
>  * Each side of the box must be touched, at least by a point, even on border

>

> there such simple solid ? And what does it looks like ?
>
> Solids are:
>  1. Milk carton (berlingot) quartic
>  2. Cone
>  3. conocuneus (coin conique) quartic
>  4. Sphere
>  5. spherical top on cylinder
>  6. Cylinder


Here is a crazy superellipsoid shape which fits the bill of 7*pi/3. Although I
do have a mathematical formula which gives an exact multiple it is very nasty
so I am not sure if this counts under your brief for the shape. I have mainly
constructed this as a point of interest that such a shape can be found and
built easily with pov csg. I am still hoping I can find a simpler shape which
wouldn't have required quite so much work to build.

Malcolm

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