rigid body solid: center of mass and tendency to topple

[ttja]

1. The problem statement, all variables and given/known data

A whimsical piece of furniture has the base shaped like a star.
Formulate the condition in terms of the location of the center of mass of
the object that the piece would not topple over. A sketch would be
helpful.

3. The attempt at a solution

Can someone help me first what the problem is asking for? I understand conceptually that the center of mass has to fall within the area support of the base, which is wherever in the area of the star base. But am i just to find the R vector to the center of mass and deem that its coordinate to fall onto the area of the plane where the base is located?

[Delphi51]

I think you would say that the center of mass must be within some cylinder centered on the vertical axis up from the center of the star base. Hmm, if it happens to be right above one of the points on the star, it can be a little further out. Maybe the volume where the c of m can be is not a cylinder but something more complicated.