The following article contains an answer for the question: What is the terrace with the fountain constructed above? , can you please find it? 

With the garden project well in hand, Ammanati turned his attentions to creating a large courtyard immediately behind the principal façade, to link the palazzo to its new garden. This courtyard has heavy-banded channelled rustication that has been widely copied, notably for the Parisian palais of Maria de' Medici, the Luxembourg. In the principal façade Ammanati also created the finestre inginocchiate ("kneeling" windows, in reference to their imagined resemblance to a prie-dieu, a device of Michelangelo's), replacing the entrance bays at each end. During the years 1558–70, Ammanati created a monumental staircase to lead with more pomp to the piano nobile, and he extended the wings on the garden front that embraced a courtyard excavated into the steeply sloping hillside at the same level as the piazza in front, from which it was visible through the central arch of the basement.  On the garden side of the courtyard Amannati constructed a grotto, called the "grotto of Moses" on account of the porphyry statue that inhabits it. On the terrace above it, level with the piano nobile windows, Ammanati constructed a fountain centered on the axis; it was later replaced by the Fontana del Carciofo ("Fountain of the Artichoke"), designed by Giambologna's former assistant, Francesco Susini, and completed in 1641.In 1616, a competition was held to design extensions to the principal urban façade by three bays at either end. Giulio Parigi won the commission; work on the north side began in 1618, and on the south side in 1631 by Alfonso Parigi.  During the 18th century, two perpendicular wings were constructed by the architect Giuseppe Ruggeri to enhance and stress the widening of via Romana, which creates a piazza centered on the façade, the prototype of the cour d'honneur that was copied in France.  Sporadic lesser additions and alterations were made for many years thereafter under other rulers and architects.To one side of the Gardens is the bizarre grotto designed by Bernardo Buontalenti. The lower façade was begun by...

"grotto of Moses"