Multiple Compatibility for Pentacubes

Introduction

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.

Nomenclature

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 ]