  A functional ansatz is developed which gives certain elliptic solutions of
the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equation. This is based on the
elliptic trilogarithm function introduced by Beilinson and Levin. For this to
be a solution results in a number of purely algebraic conditions on the set of
vectors that appear in the ansatz, this providing an elliptic version of the
idea, introduced by Veselov, of a V-system.
  Rational and trigonometric limits are studied together with examples of
elliptic V-systems based on various Weyl groups. Jacobi group orbit spaces are
studied: these carry the structure of a Frobenius manifold. The corresponding
almost dual structure is shown, in the A_N and B_N and conjecturally for an
arbitrary Weyl group, to correspond to the elliptic solutions of the WDVV
equations.
  Transformation properties, under the Jacobi group, of the elliptic
trilogarithm are derived together with various functional identities which
generalize the classical Frobenius-Stickelburger relations.
