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# rigid body dynamics - Combining Moment of Inertia Tensors

In a physics simulation of rigid bodies, if I have a cube with a known mass and moment of inertia tensor, and I attach it to another cube with a known mass and moment of inertia tensor such that its transform relative to the second cube is constant (put simply, they are stuck together completely), how can I compute the moment of inertia tensor of the resulting body? How would I compute it if I continued to add cubes in different places? Keep in mind that I'm not just stacking them, I could end up with a strange U or T or L shape, for instance. The cubes' rotation will all be identical, i.e. they will always be connected face-face, never vertex-face or edge-face or anything. They are all the same size, but may vary in mass. The faces will always connect in such a way that four vertices on one cube will touch four vertices on another cube (in other words, I won't have one cube poking out from behind another cube, they will line up nicely). The bodies have constant density.

Could I possibly use the Parallel Axis Theorem? Maybe find the center of mass of the combined bodies and finding the moment of inertia tensor for each body through that axis, and then somehow adding all the matrices together?