  Using the theory of "higher structure maps" from generic rings for free
resolutions of length three, we give a classification of grade 3 perfect ideals
with small type and deviation in local rings of equicharacteristic zero,
extending the Buchsbaum-Eisenbud structure theorem on Gorenstein ideals and
realizing it as the type D case of an ADE correspondence. We also deduce
restrictions on Betti tables in the graded setting for such ideals.
