The Regia was the seat of authority for the Pontifex Maximus or chief priest, the administrative and spiritual superior of the Vestals, until Augustus assumed those duties and moved the official residence to the Palatine. It was restored in 36 BC, the curious trapezoidal shape an attempt to maintain the building's orientation to the points of the compass and still fit behind the Temple of Divine Julius.
More so than even the Temple of Concord, which still has remnants of its magnificent frieze and capital, the Regia is not nearly so photogenic. A measure of how difficult it is to represent can be seen at Wikipedia, which still uses the illustration from the now defunct online game SPQR that I created for my essay in 1997.
