Not all interesting architectural geometry is intentional. Fire escapes, utility lines, parking structures, and loading docks weren't designed with photography in mind, but they often produce some of the most striking geometric compositions in a city, precisely because they're functional rather than decorative.
Function creates its own order
Structures built purely for utility — a stairwell, a grate, a row of identical windows — tend to follow a strict internal logic, and that logic often translates into strong, legible geometry in a photograph, even without any artistic intention behind the original structure.
Look up, and look down
Most people experience a city at eye level, which means the geometry above and below eye level — ceilings, undersides of bridges, patterns in pavement — goes largely unphotographed. Deliberately looking up or down, rather than only straight ahead, tends to reveal compositions that are easy to miss otherwise.
