Among Cortona's more important architectural projects are the church of Santi Luca e Martina (completed in 1664, the church of the Accademia di San Luca, located in the Roman Forum. While Cortona was "principe" or director of the Accademia from 1634–38, he obtained permission to dig in the crypt of the church, which led the likely mistaken finding of remains attributed to the first century Roman martyr and Saint Martina. This discovery led to further patronage for construction of the church. The layout is almost a Greek cross, with four nearly identical wings extending from the striking central dome. Much of the ground structure is undecorated, above intricately decorated. The overwhelmingly vertical decoration of the facade is granted liveliness by horizontal convexity. In his will, this bachelor called this church his "beloved daughter".