Chad Schoen (2007) used deformations to construct a family of smooth complex algebraic surfaces S with invariants \chi=2, q=4 and K^2=16 with some remarkable properties. Then C. Ciliberto, M. Mendes Lopes and X. Roulleau (2015) showed that the canonical map of S is a double covering of a degree 8 surface X in P^4 with 40 double points. In this talk I will explain how to construct the Schoen surfaces explicitely, by computing equations for the surfaces X. There is an interesting connection to the classical Segre cubic and Igusa quartic threefolds.