identical, where the single fertilised egg splits sometime
in the first 12 days after conception. If it splits in the
first 3 4 days, the twins have separate placentas. In
the most common situation, the split occurs 4 8 days
after conception and the twins share the one placenta. A later
split can lead to more complications and Siamese (conjoined)
twins are those where the splitting process begins after 12
days.

(From D.A. Hay (1985) Essentials of Behaviour Genetics. Oxford:Blackwells,
p218)
It is important to note that identical twins are only identical
genetically and there are many physical and behavioural characteristics
less determined by heredity where they may differ considerably
and where non-identical twins may be very similar. Thus we
shall use the more neutral terms DZ (for dizygotic or two-egg
twins) instead of non-identical and MZ (for monozygotic or
one-egg twins) instead of identical.
Higher multiples can be any combination of MZ and DZ. For
example two eggs may be fertilised (making DZ twins) and then
one developing embryo splits to form a set of MZ twins. It
would be possible to have identical triplets where one early
embryo splits and then one of these splits again.
We have such a family in Australia which interestingly resulted
from fertility treatment. The doctors and initially the parents
assumed the girls must be DZ, resulting from three eggs being
fertilised. By the time they were three, the mother was pretty
convinced they were MZ and blood tests confirmed this. There
has been some discussion that the process of in vitro fertilisation
may make splitting of the embryo and the formation of MZ twins
more likely.