The puzzle 'Octetra' was invented by Viktor Genel around 2001. This puzzle consists of 6 polysphere pieces. One can select four pieces of the set to form an octahedron, or four different pieces from the same set of 6 to make a tetrahedron.
George Bell independently came up with the same octahedron design in 2010. The name "U'Y" derives from the shape of the pieces. It can be pronounced either "You-Why" or "You-We" to rhyme with "Screwy".
This puzzle is unusual in that assembly requires coordinate motion where three pieces rotate as they go together onto the fourth piece. Care must be taken when disassembling, because if the proper coordinate motion is not initiated one of the pieces could break. I do not believe this puzzle can be assembled with completely rigid pieces, a slight flex seems to be needed. Once together the assembly is quite tight, and spinning will not open the puzzle.
The photos below show the original six Octetra pieces, as well as the four used for the tetrahedron construction. The length of the long rod can be determined by making sure the sphere centers are separated by a distance equal to the square root of 2 times the sphere diameter. Assembly of the tetrahedron requires a very tight move that might not be possible in wood.