Wholly or partly open to the sky; having a roofless central space.
Etymology: from Greek hypaithros (hypo- under + aither air, ether, sky).
By far, the most common use of the word is in discussions of Greek temples, usually in reference to a treatise on architecture from Vitruvius.
Although I've never seen it used in this context, I would think most football and baseball stadiums are hypaethral (at least when the weather's good).
"Shall the mind be a public arena, where the affairs of the street and the gossip of the tea-table chiefly are discussed? Or shall it be a quarter of heaven itself, — an hypæthral temple, consecrated to the service of the gods?"
- Henry David Thoreau, "Life Without Principle"
For my part, the phrase "hypaethral temple" revives images of the field of tall grass I played in when I was a kid: I would flatten a small area and then lie down, hidden from the rest of the world, and stare up at my own personal cylinder of sky.