Exact results are obtained for a square lattice fifteen-vertex model and related O(n) model recently proposed by Nienhuis (1990). The partition function per site and finite-size corrections are obtained, along with the critical exponents via the Temperley-Lieb equivalent six-vertex model. The exact exponents nu =⁴/₇ and gamma =⁶/₇ follow in the limit n=0 for even system sizes. Odd system sizes are also discussed. The fifteen-vertex model is also the vertex formulation of the anisotropic, or q-deformed, spin-1 biquadratic model.