  We classify all regular solutions of the Yang-Baxter equation of eight-vertex
type. Regular solutions correspond to spin chains with nearest-neighbour
interactions. We find a total of four independent solutions. Two are related to
the usual six- and eight-vertex models that have R-matrices of difference form.
We find two completely new solutions of the Yang-Baxter equation, which are
manifestly of non-difference form. These new solutions contain the S-matrices
of the AdS2 and AdS3 integrable models as a special case. Consequently, we can
classify all possible integrable deformations of eight-vertex type of these
holographic integrable systems.
