This (and its rotations) are the only solution of the puzzle
without gaps between pieces.
It has beautiful three-hold symmetry.
There are many ways to put nine pieces if we allow gaps between
pieces.
However, we found only solutions that have a T at the center of the box.
It is open whether other kind of solutions exist to this puzzle.
We enumerated solutions with a T located at the center of the box.
There are 512 solutions of this form.
(We identify those equivalent by horizontal rotation of the cube, and do not
identify mirror images.)
There are 276 solutions modulo mirror equivalence.
We have 52 solutions if we identify those equivalent through three-dimensional rotations.
- Yoshiaki Araki at Tessellation Design draw
picture of 136 solutions
(they are the 276 solutions with the central T fixed)
-
Python Program for this calculation
and
link to Google Colab
- It is misterious that 512 = 2^9, isn't it?
It is still open whether there is a solution that does not place a T at the center of the box.
This puzzle is related to the fact that the three diagonals of T are orthogonal
and T can be arranged so that all the 6 vertices are on the axis of coordinates.
H and T form a three-dimensinoal tiling, as this picture shows.
In this tiling, a T touches 8 pieces around it and
The solution is such nine pieces put into a box.