# 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.

Back to Multiple Compatibility
< Polyform Compatibility
< Polyform Curiosities

Col. George Sicherman
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