  A polarity of a projective plane is a map, often assumed to be involutive,
mapping a generic point to a generic line and reciprocally. The most classical
polarity is the polarity with respect to a conic, but other exist: the harmonic
polarity with respect to a triangle, the polarities with respect to high-degree
algebraic curve, the polarities with respect to a convex set. In this article,
we introduce a polarity with respect to a triangle motivated by a question on
duality of projective frames. We show that the four polarities above apply to a
triangle and in fact coincide. This result is an opportunity to review nice
concepts of projective geometry, linear algebra and convex geometry.
