# Pentacubes in a Box Without Corners

## Introduction

A pentacube is a solid made of five equal cubes joined face to face. There are 23 such figures, not distinguishing reflections and rotations:

The six blue tiles have distinct mirror images. Kate Jones's systematic names are shown in green. Donald Knuth's names are shown in red.

All but two pentacubes can tile a rectangular prism, or box; see Pentacubes in a Box. Here I show that every pentacube can tile a box with the corner cells removed. The cross-sections are shown from back to front. If you find a smaller solution for a pentacube, please write.

## Solutions

2 tiles, 2×3×3

2 tiles, 2×3×3

2 tiles, 2×3×3

20 tiles, 3×6×6

8 tiles, 2×4×6

8 tiles, 3×4×4

9 tiles, 1×7×7

8 tiles, 2×4×6

8 tiles, 2×4×6

4 tiles, 1×4×6

### M

312 tiles, 7×8×28

10 tiles, 1×6×9

4 tiles, 1×4×6

8 tiles, 2×4×6

8 tiles, 2×4×6

### S

8 tiles, 2×4×6

#### Without Reflection

248 tiles, 6×8×26

### T

92 tiles, 3×12×13

2 tiles, 2×3×3

56 tiles, 6×6×8

12 tiles, 1×8×8

1 tile, 1×3×3

8 tiles, 2×3×8

### Z

88 tiles, 4×8×14

Last revised 2016-02-10.

Back to Polyform Tiling < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]