5x5x5 Pentacube Puzzle

The buttons for mirroring, rotation, and translation let you place the pentacubes in any way you want.

Once you have placed a pentacube, hit the "create next" button. This will cause another pentacube to appear outside the 5x5x5 box.

This new pentacube will then be the one you are manipulating. However, you can select to manipulate any of the other visible pentacubes—simply click the corresponding colored button. If you select a pentacube number which has not been created yet, nothing will happen.

You can separately select to show the floor, the wire frame, or the colored arrows that mark the three coordinate axes (red = axis, blue = axis, green = axis).

This Demonstration is based on the article by the author, "The Primes of a Certain Pentacube", Journal of Recreational Mathematics, 26(1), 1994 pp. 1–2.

Tiling the 5x5x5 cube with the pentacubes given here is also one of the topics of the author's Zillions game "Comacube", which contains 11 such puzzles using various pentacubes.

It is easy to make the pentacubes from wood, so you can try to solve the problem hands-on as well.

When clicking the "+" or "-" button, pause between clicks; otherwise the system can get stuck.

Also, when many pentacubes are displayed, the system's reaction time slows down, so you have to slow down your clicks as well.