Israeli tour guide Shmuel Browns has done some investigation and come to the conclusion that the monumental building at the Herodium was a nymphaeum.  He has posted his research, with numerous illustrations, here

You may recall that archaeologist Ehud Netzer once proposed that this structure was Herod’s tomb. 

Since the location of the burial place on the slope of the mountain, the question is open once again, and Browns’ proposal seems like the right one.  It would be just like Herod to construct a palace in the wilderness complete with swimming pool and monumental fountain.