  We construct Moufang sets, Moufang triangles and Moufang hexagons using inner
ideals of Lie algebras obtained from structurable algebras via the
Tits--Kantor--Koecher construction. The three different types of structurable
algebras we use are, respectively:
  (1) structurable division algebras,
  (2) algebras $D \oplus D$ for some alternative division algebra $D$, equipped
with the exchange involution,
  (3) matrix structurable algebras $M(J,1)$ for some cubic Jordan division
algebra $J$.
  In each case, we also determine the root groups directly in terms of the
structurable algebra.
