The Neptune Fountain is a Mannerist work that was built to pay homage to the pontificate of Pius IV. The main purpose for which it was erected is to symbolize the Pope's dominion over the world, which around him sows wealth and fertility, just as the god Neptune dominates the waters.
At the base of the central structure there are four Nereids (sea nymphs of Greek mythology); rising up we find pontifical emblems and four cherubs (naked children with wings) holding dolphins symbolizing the Ganges, the Nile, the Amazon and the Danube.
It is said that Giambologna wanted to represent the Neptune with the largest genitals and, in order not to incur the censorship of the Church, he studied a pose such that from a certain angle the thumb of a hand seems to sprout from the lower abdomen. The point in the square from which one has a better view of this effect is marked by a black stone: "the stone of shame".