This mechanism is similar to the plug I posted yesterday. However, it uses a separately printed dowel — a flat, chamfered square block. It features two small bumps for a better friction fit in the joined parts. Those also ensure you hear that satisfying snap when putting parts together. 
To join two half-cubes at one of their square faces, they sandwich a full dowel between them, to align the seam and merge them using the dowel’s friction.
The slot in the objects to join must always be printed vertically when on a side, so overhangs are guaranteed to not exceed 45°. When on the bottom or the top, it should be rotated 45° to maximize distance from the object’s sides.
The slots are created using the dowel shape with a small tolerance gap added. The dowel shape is used twice, so the small groove for the bump is on both sides.
See Square Dowel on GitHub for related files, including the SCAD source.