Almost joints are designed with one orientation in mind or maybe two. But this joint—the Kawai Tsugite joint—fits perfectly in three different ways. How does that work?
The three-way aspect of this joint is based on the rotational symmetry of a cube about an axis going through opposite corners,” explains Wandel.
If you spin this cube between your fingers by 120 degrees (1/3 of a turn), it will occupy exactly the same space as before.
Now, if I cut the cube in half, through a plane perpendicular to that axis, You can rotate one side of the cube by 120 degrees and the two halves will still form a cube,this is the basis of this joint.
But this joint is really not a useful woodworking joint. Wood is strongest along the grain, and this joint doesn’t take advantage of that.