I've been thinking about finding the moments of inertia of 4D rotatopes. This might have been done before, but I'll show them anyway.
A moment of inertia about an axis, or plane is
I = Integral (r^2 dm),
which is a constant for any solid.
The r^2 is derived from K =1/2 mv^2, and v = f cross r
where f is the angular frequency. So assuming we keep the same definition for kinetic energy, we shouldn't change this to r^3.
Here's the derivations for a cylinder and a sphere
http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2
http://hyperphysics.phy-astr.gsu.edu/hbase/isph.html#sph2
For a cubinder with radius R, length L1 and tridth L2, rotating about the two linear axes, we can follow the same method as for the cylinder, and end up with the same inertia.
We can find the inertia of a spherinder by integrating the inertia of a sphere over the length. The length is included in the mass, so it gets cancelled out, and the inertia is identical to a sphere.
These are encouraging results, but the glome and the duocylinder might be more difficult. It's getting late, so I'll try them tomorrow.