Multiple Compatibility for Pentacubes


A set of polyforms is compatible if there exists a figure that each of them can tile. Here are minimal figures that can be tiled by a given number of pentacubes. If you find a smaller solution or one that can be tiled by more pentacubes, please write.

For other polyforms, see Multiple Compatibility for Polyominoes, Multiple Compatibility for Polyiamonds, and Multiple Compatibility for Polyhexes.


I use these names for the 29 pentacubes:

6 Pentacubes

2 Tiles

Mirror: B G′ J′ P Q R′

11 Pentacubes

4 Tiles

Mirror: B E F G′ J′ P Q R S Y Z

15 Pentacubes

6 Tiles

Mirror: A B E′ G H H′ J K M N P Q R R′ U

16 Pentacubes

8 Tiles

20 Pentacubes

16 Tiles

21 Pentacubes

24 Tiles

26 Pentacubes

240 Tiles

A 10×10×12 solid rectangular box can be tiled by every pentacube but G, G′, and X. Those three pentacubes cannot tile any box.

Last revised 2023-08-20.

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Col. George Sicherman [ HOME | MAIL ]