Imaginary Cube

Puzzle Explanation

Imaginary Cube Puzzle 3H = 6T — assembled view

There is only one gap‑free solution to this puzzle (up to rotation of the box). That solution forms the elegant shape shown here, possessing a clear three‑fold rotational symmetry.

Pieces arranged on the three‑dimensional coordinate axes

A key reason this packing works is that the T‑pieces can be arranged so that every vertex lies on one of the three coordinate axes. See the slides below for a detailed explanation.

Another completed configuration of the puzzle

The puzzle is also connected to the fact that the two solids H and T can together tile three‑dimensional space. For details, please refer to the slides below.

Slides

If the embedded viewer is hard to read, download the  PDF of the 2020 mock‑lecture slides .