  Several asteroids are known to be shaped like toy tops. This paper models
Top-Shaped Asteroids (TSAs) as Homogeneous Symmetric Lenses (HSLs), and derives
their rotational, self-gravitational, and total energies as functions of their
mass, density, and angular momentum. Then we raise, test, and ultimately reject
the hypothesis that TSAs take the shape of lowest total energy, subject to the
constraint that they keep the same mass, density, and angular momentum, while
remaining HSLs. Other processes must control the shapes of TSAs. For
completeness, we also describe a Core-Mantle Model for TSAs, as well as an
Inverted Core-Mantle Model, and derive their self-gravitational energies, along
with their rotational energies. The gravitational potential at the center of an
HSL then is derived.
