Interlocking 20-Ball Tetrahedron

Assembly Solution

Begin with two identical pieces, we will use the two on the right in the above photo. Place one on a table so that the obtuse end lies flat (first photo below). Then place the second piece on top, oriented 90 degrees from the first piece, with the 90 degree angle down. The second piece does not lie flat on the table, but lies in the air against the 90 degree angle of the first piece.

This results in the following strange shape (below), which is the key to the entire assembly. It is in fact half a tetrahedron, and if you took its mirror image it would fit right into it to make a full tetrahedron. The balls at the top and bottom are two of the four corners of the tetrahedron.

We now place the final two pieces. To orient them correctly it helps to remember that the balls at the obtuse ends become the corners of the tetrahedron.

The final piece is now the trickiest to place, because it must be snapped into place. Grab it as shown below and slide in the 90 degree end first, so that its position is as in the second photo below.

As indicated by the red arrow, push this piece into place. You should feel some resistance as it snaps into position. Congratulations, you have aseembled the puzzle! Give it a toss in the air and it should stay together.

Disassembly Solution

The only trick here is to push in the proper direction on one of the corners so that the first piece pops off. Orient the tetrahedron properly, and push the corner ball as indicated by the red arrow. It is best to do this with your other hand!

After the first piece is loose, the puzzle will fall apart.