  The embedded contact homology (ECH) of a 3-manifold with a contact form is a
variant of Eliashberg-Givental-Hofer's symplectic field theory, which counts
certain embedded J-holomorphic curves in the symplectization. We show that the
ECH of T^3 is computed by a combinatorial chain complex which is generated by
labeled convex polygons in the plane with vertices at lattice points, and whose
differential involves `rounding corners'. We compute the homology of this
combinatorial chain complex. The answer agrees with the Ozsvath--Szabo Floer
homology HF^+(T^3).
