The Cog Maze (歯車, Haguruma, Gear) is an area accessible from the Construction Frame Building.
The cog maze is a teleport maze consisting of floating gears of various sizes, serving as platforms. Rotating Phillips-head screws on each platform act as portals between other gears.
A slightly shorter screw on a platform to the northwest leads to the Construction Frame Building, while a bent screw on another platform connects to the Forest Pier. When interacting with this screw for the first time, you'll trigger a short cutscene, showing the basement door in Urotsuki's Dream Apartment being unlocked.
A third shorter screw exists deeper inside the platform maze but currently teleports you to itself - effectively a dead end. A platform in the west constructed of three cogs with one screw in the middle is home to a brown walking drawing mannequin which will take you to Nail World.