  We show that an orientable pseudo-Anosov homeomorphism has vanishing
Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its
dilatation is not reciprocal. We relate this to works of Margalit-Spallone and
Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of
pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing
Sah-Arnoux-Fathi invariant. In particular, we give new infinite families of
such maps in genus 3.
