  In this paper, we classify all spin models for singly-generated Yang-Baxter
planar algebras in terms of certain highly regular graphs. Using Liu's
classification of singly generated Yang-Baxter planar algebras, this classifies
all spin models for the Jones polynomial, the Bisch-Jones planar algebras, and
the Kauffman polynomial. This simplifies and clarifies Jaeger's classification
of spin models for the Kauffman polynomial. In particular, we completely avoid
the opaque and computationally-taxing concept of "formal self-duality"; we also
explain the numerous exceptional cases in Jaeger's classification by
demonstrating a new, discrete two-parameter family of spin models for the
Bisch-Jones planar algebras.
