Sequel to Shape of a Habitable Neutron Star. Maybe this'll be easier to figure out an answer to--or maybe the answer will end up being nicer, in the slightly less extreme case of a white dwarf.
A white dwarf spinning Sufficiently Fast should eventually end up with an equatorial bulge that has weak enough gravity for electron-degenerate matter to start "re-inflating". Spin it even faster, and eventually you'll get a rim with low enough gravity that a human could stand on it (supposing this is a trillion-year-old white dwarf that has cooled off so the human doesn't fry, anyway).
You won't get the variety of elements that you would from decaying neutronium, but that's OK--spinning up a star that much would have to be done artificially, so if we want it to actually be habitable, just assume the Alien Space Bats imported some suitable planetary crust material to layer on top.
But... what might that actually look like? What's the final shape? Would there actually be room to stand on that equator, or would it be too thin to inhabit? It would be relatively simple to work out the shape of an oblate spheroid of uniform density, or the equipotential surface around a point mass, but like the neutron star, this thing is not really close to either ideal.
If a precise answer is impractical to give, I would still appreciate references that might help me figure it out.
EDIT: This is not a duplicate, as there is no guarantee that answers to the previous question would be applicable to this one, or vice-versa. Neutron stars and white dwarfs are very different kinds of objects with completely different equations of state.
