belvederes
/ˈbɛlvɪdɪə/
noun
A summer house or open-sided gallery, typically at rooftop level, commanding a fine view.
Here NGP proposes inserting what is effectively a completely new glazed building into the hole, rising on tall columns to provide an inhabited roof level with a cyclopean belvedere of a west wall.
arbour,shady place,leafy shelter,alcove,recess,pergola,grotto,sanctuary