In a painting:
there is this formula of volume:
$$V = \frac{\sqrt{3}}{3}\pi r^3$$
It seems to me this is the formula of the volume of some polyhedron inscribed or circumscribed to a sphere of radius $r$, but I am not expert of the field.
I had the task of finding the meaning of the different formulas, that were taken from a web site whose address has been lost, so I need to find the regular solid that corresponds to such formula, if it exists.
So I am asking help from somebody more expert then me in the field of geometry of solids, if there is some "significant" solid with the volume given by that formula.
Note: this question is twin of another question.
Thanks a lot in advance.
(Converting a comment to an answer, as requested.)
The appearance of $\pi$ suggests that this is not the formula for the volume of a (flat-sided, straight-edged) polyhedron, whether inscribed or circumscribed about a sphere. Rather, there must be a circular component.
@LeeDavidChungLin's commented suggestion ---a cone of radius $r$ and height $\sqrt{3}\,r$--- seems to be the "most natural" one: the target volume decomposes as $$\frac13\cdot \pi r^2 \cdot \sqrt{3}\,r \;=\; \frac13\cdot(\text{area of base})\cdot(\text{height})$$
I'll note that such a cone arises from revolving an equilateral triangle of side $2r$ about an axis of symmetry.