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 ]