"on the edifice" is correct and usable in written English.
For example, you could use it in a sentence such as, "The artist painted a mural on the edifice of the old cathedral."
Yet he had, in a way, been even more deeply affected by the new physics than his contemporaries, because he saw that Einstein's observations weren't just new ones resting on the edifice of old ones.
"It's like we tapped on the edifice and it crumbled," Mr. Brown said, shaking his head.
"A devastating bomb has fallen on the edifice of Europe," wrote the Italian newspaper Corriere della Sera.
Thurgood Marshall's assault on the edifice of segregation had been confounded by the question of whether the Fourteenth Amendment prohibited racial segregation.
Fukuyama's thesis proposes a kind of fatalism that is worth resisting, but it is not an intellectual ornament on the edifice of American hegemony — or a rationale for invasion, occupation, and conversion of the non-Westernized world.
The eruptive deposits on the edifice of the Ontake volcano were investigated along trails on the SE side (Ohtaki Trail), the NE side (Kurosawaguchi Trail), the N side (Ninoike Gonoike Trail), and the summit area (Figs. 1, 4).
Mr. Finkelman retained many of the original architectural details, including a limestone-clad entranceway and the greater part of a long limestone cornice on the front of the edifice.
The city's leading guilds were assigned niches on the exterior of the edifice in which to place statues of their patron saints, each commission aiming to outdo its predecessor in artistic excellence.
Flow data forms the base on which much of the edifice of water management is raised.
In this study, we consider the system in which degassing magma is supposed to be located far below the water table at around sea level (more exactly, it depends on the permeability of the edifice) and hydrothermal fluid ascends intensively through the central conduit.
The VAL was decreased to 2 on September 11 , 2015 since inflation of the edifice seemed to have halted since August.
