Other orientations of the cube preserve the similarity of the small tents to BT. I imagine a program that computes the moment of BT given a vector p in the cube coordinates which defines the base of BT as {x | p∙x = 1}. zi < 0. (We can forego these inequalities and transcend this limitation if we add in another similar tent for each i for which the inequality fails. In general)

To apply this to the buoyancy and stability problem we must compute the total system energy. The total energy is the moment of the portion of the cube above the water times the cube density plus the moment of the portion below water times (1 − density). Both moments are taken as positive here.

This formulation leaves the density to be computed rather than given. For given inputs there will be a volume above the water and (1 − that) below the water.

The volume of BT is the product over all i’s of √(s2 + zi−2)/3! . The altitude of the origin over the plane is

The coordinates of the vertices of the base of BT are (a/zi)(xi, yi, 0).