  A conjecture of Freiman gives an exact formula for the largest volume of a
finite set $A$ of integers with given cardinality $k = |A|$ and doubling $T =
|2A|$. The formula is known to hold when $T \le 3k-4$, for some small range
over $3k-4$ and for families of structured sets called chains. In this paper we
extend the formula to sets of every dimension and prove it for sets composed of
three segments, giving structural results for the extremal case. A weaker
extension to sets composed of a bounded number of segments is also discussed.
