The "Wander About a Big World in Whatever Order You Fancy Solving Puzzles To Get New Areas You Can Explore and Solve Puzzles in or Whatever" genre Fez, Antichamber and Kirby and the Amazing Mirror belong to needs a better name than WAaBWiWOYFSPTGNAYCEaSPioW. Let's come up with one because I think with Antichamber's coming it sort of feels like an actual genre to me now rather than being "Just the way Fez is." It's related to a Metroidvania only with no or next to no roadblocks requiring upgrades. Well, Antichamber has a few upgrades but you can get them in 5 minutes if you know what you're doing. Also I think it's a really cool genre. Fez, Antichamber, Kirby, all really fun games with big worlds it was always just fun to explore. Hell, they're fun to explore even when you've already juiced them to completion. I know because I lost Fez save data twice (updates!) and played that Kirby game a few times over the years. And I did wander around Antichamber a fair bit even after I had found everything that's to be found.
They're rich worlds filled with things to discover through exploration. I mean that both in the sense that you discover interesting areas and you discover things about the mechanics of the world. You also discover puzzles and their solutions very organically with basically no pressure as you're free to back out at any time. That's a really good property.
Anyway, names. Would "Fezchamber" be too terrible? How about Antimirror? Hmmm... Fezby & The Anti Genre. No, that's no good. Hmmm... Best I got is Fezchamber. What do you have?