# Cell Shifts for Pentacubes

## Introduction

A *polycube* is a solid made of equal cubes joined
face to face, and a *pentacube* is a polycube with 5 cells.
There are 29 pentacubes, distinguishing mirror images:

A *cell shift* for a polycube is a pair of arrangements of
copies of the polycube that differ by a single cell.
Here I show the shortest cell shift for each pentacube,
not letting the tiles be reflected.
I try to use as few tiles as possible.
If you find a shorter cell shift or a solution with fewer tiles, please write.

See also Cell Shifts for Polyominoes.

## 1

## √2

## 2

## 5

## No Solution

Mike Reid proved that the **X** pentacube cannot shift a single cell.

## With Reflection

If the pentacubes may be reflected, we can use fewer tiles.
### 1

### 2

Last revised 2022-11-28.

Back to Polyform Cell Shifting
<
Galvagni Figures for Polyforms
<
Polyform Curiosities

Col. George Sicherman
[ HOME
| MAIL
]