Abstract. We present Lambda Twist; a novel P3P solver which is accurate, fast and robust. Current state-of-the-art P3P solvers find all roots to a quartic and discard geometrically invalid and duplicate solutions in a post-processing step. Instead of solving a quartic, the proposed P3P solver exploits the underlying elliptic equations which can be solved by a fast and numerically accurate diagonalization. This diagonalization requires a single real root of a cubic which is then used to find the, up to four, P3P solutions. Unlike the direct quartic solvers our method never computes geometrically invalid or duplicate solutions. Extensive evaluation on synthetic data shows that the new solver has better numerical accuracy and is faster compared to the state-of-the-art P3P implementations. Implementation and benchmark are available on github