Claim: In the late 1780s, Antinori was commissioned by Pope Pius VI, to make a better layout for the piazza and had the fountain and the Dioscuri moved; then some time between that original fountain was lost and in 1818, a new one was commissioned by Pope Pius VII.
Evidence: In the late 1780s by Antinori, was commissioned by Pope Pius VI, to make a better layout for the piazza and had the fountain and the Dioscuri moved, and included the large Obelisk which had been moved from the Campus Martius in the design. Some time between, that original fountain was lost, and, in 1818 a new one, which can be seen today, was commissioned by Pope Pius VII and was designed by Raffaele Stern using an ancient granite Roman shell that had been found in the 16th century supported on top of a large basin.