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In this work, we employ the algebraic-differential method recently developedby the author to solve the Yang-Baxter equation for arbitrary fifteen-vertexmodels satisfying the ice-rule. We show that there are four different familiesof such regular $R$ matrices containing several free-parameters. Thecorresponding reflection $K$ matrices, solutions of the boundary Yang-Baxterequation, were also found and classified. We found that there are threedifferent families of regular $K$ matrices, regardless of what $R$ matrix wechoose.

Fifteen-vertex models with non-symmetric $R$ matrices