We study eggs in PG(4n - 1, q). A new model for eggs is presented in which
all known examples are given. We calculate the general form of the dual egg
for eggs arising from a semifield flock. Applying this to the egg obtained
by L. Bader et al. (1999, J. Combin. Theory Ser. A 86, 49-62) from the Pen
ttila-Williams ovoid, we obtain the dual egg, which is not isomorphic to an
y of the previous known examples. Furthermore we give a new proof of a conj
ecture of J. A. Thas (1994, J. Combin. Theory Ser. A 67, 140-160) using our
model and classify all eggs of PG(7, 2) which is equivalent to the classif
ication of all translation generalised quadrangles of order (4, 16). (C) 20
01 Academic Press.