Three Pairs

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(left: Mahogany, 6 pieces, 4 inches
right: Cherry, 6 pieces, 4 inches;
the one on the left was purchased at auction in 2001, the cherry one on the right is
one of 6 puzzles purchased during a visit with the designer in the early 1980's;
he called this cherry one a "crude loose-fitting prototype",
but of course it has terrific fit, and although it has some nicks
and pencil marks on the interior edges, overall it is a beautiful puzzle)

Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:
"To disassemble, grasp the opposite pairs of pieces, and gently pull and wiggle until you discover the combination that separates it diagonally into halves. The wiggle the pieces apart until you discover the strange action that separates each half into three pieces."
The name is a joke that implies that each of the three axes is formed from some sort of pair configuration; that is, the implication being that the puzzle works something like a burr, where pieces slide in and out parallel to the three axes. In fact, it splits into two halves of 3 pieces each along a diagonal plane. Then, the two halves each come apart by simultaneous motion of all three pieces. Below, the left shows the two halves and the right shows one of the pairs: