I’m engaged on a good 9-sided die and I settled on a design the place you choose three edges of a dice the place the 2 sides that one edge touches do not overlap with any of the opposite sides touched by the opposite edges, then chamfer these edges off. This ends in three rectangular faces (beforehand edges) and 6 irregular pentagonal faces (beforehand squares), and I believed it could be so simple as making all of the faces have the identical space. But no, once I did that, the oblong faces (or not less than their facilities) had been nearer to the middle of gravity than the pentagonal faces, and so had been landed on extra typically than the pentagonal faces (or not less than the oblong faces landed as the bottom of the cube, and an edge on the highest of the cube.) I’m comparatively positive that the answer to this downside is to divide the realm of the oblong face by the space of that face’s middle to the middle of mass, do the identical for the irregular pentagonal faces, then make these two ratios the identical.

Assuming that B is the middle level of the primary form, A is the realm of the primary form, and A’ is the realm of the second form, discover a answer that satisfies this equation: A/D=A’/D’

Please assist, I’m not that good at math.