Regarding that axiom, an interesting link is here.
This building at Fourth Avenue and Eighth Street was the parish school from 1919 to 2005. It is now rented to the New York City Board of Education. There are at least several public school buildings with crosses in our city. The Brentwood Josephites taught in this parish since 1884.
In Brooklyn there are two parishes named St. Thomas Aquinas. The other one is in Flatlands, established almost at the same time, but before Flatlands was part of the city of Brooklyn.