  A new proof of the non-rationality of a generic cubic threefold is given as
follows: If a generic cubic threefold were rational then the associated
intermediate Jacobian would be a product of Jacobians of curves. We degenerate
a generic cubic threefold to the Segre Cubic Threefold and so there is a
degeneration of intermediate Jacobians as well. Associated to the degenerating
family of Pryms is a unimodular system of vectors. Rationality of the generic
cubic threefold would imply that the unimodular system would be cographic
dicing. However, we show that the unimodular system obtained is a well known
symmetric non-cographic dicing called E_5.
