  We obtain, by a direct computation, explicit descriptions of all principally
polarized semi-abelic varieties of torus rank up to 3. We describe the geometry
of their symmetric theta divisors and obtain explicit formulas for the
involution and its fixed points. These results allow us to give a new proof of
the statements about the dimensions, for small genus, of the loci of ppav with
theta divisor containing two-torsion points of multiplicity three. We also
prove a result about the closure of this set. Our computations used in our work
arXiv:1103.1857 to compute the class of the closure of the locus of
intermediate jacobians of cubic threefolds in the Chow ring of the perfect cone
compactification of the moduli space of principally polarized abelian
fivefolds.
