# Tetracube-Pentacube Pair Oddities

## Introduction

A *tetracube* is a solid made of 4 equal cubes joined
face to face.
There are 8 tetracubes, counting distinct mirror images.

A *pentacube* is a solid made of 5 equal cubes joined
face to face.
There are 29 pentacubes, counting distinct mirror images.

A polyform *oddity* or *Sillke Figure*
is a polyform with binary symmetry at least,
tiled by an odd number of copies of a given polyform.

Here I show polycubes with full symmetry and an odd number of cells,
formed by joining copies of a given tetracube and a given pentacube.
The solutions are the smallest known to me.
The figures shown are the numbers of tiles used.

If you find a smaller solution, please write.

See also Pentacube Pair Oddities.

## Table of Results

| A | B | E | F | G | H | I | J | K | L | M | N | P | Q | R | S | T | U | V | W | X | Y | Z |

I | 119 | 119 | 119 | 117 | 125 | 117 | 125 | 111 | 117 | 125 | 87 | 117 | 111 | 111 | 117 | 117 | 125 | 117 | 125 | 125 | 267 | 125 | 125 |

K | 63 | 81 | 27 | 63 | 113 | 57 | 125 | 27 | 57 | 93 | 25 | 57 | 27 | 63 | 63 | 93 | 93 | 81 | 73 | 27 | 111 | 113 | 81 |

L | 27 | 67 | 27 | 75 | 75 | 27 | 75 | 27 | 75 | 75 | 93 | 73 | 27 | 27 | 27 | 75 | 75 | 27 | 75 | 75 | 105 | 75 | 27 |

N | 81 | 81 | 81 | 99 | 81 | 117 | 125 | 81 | 119 | 109 | 117 | 79 | 113 | 113 | 117 | 117 | 81 | 75 | 81 | 117 | 117 | 105 | 81 |

Q | 111 | 81 | 81 | 117 | 125 | 117 | 61 | 81 | 119 | 111 | 225 | 117 | 113 | 113 | 117 | 117 | 117 | 119 | 27 | 213 | ? | 117 | 123 |

S | 75 | 75 | 81 | 81 | 75 | 75 | 109 | 75 | 75 | 87 | 129 | 81 | 27 | 75 | 75 | 75 | 81 | 75 | 67 | 75 | 147 | 87 | 75 |

S′ | 81 | 75 | 75 | 81 | 75 | 87 |

T | 57 | 49 | 49 | 57 | 57 | 57 | 57 | 57 | 57 | 57 | 25 | 57 | 27 | 57 | 57 | 57 | 57 | 27 | 57 | 57 | 25 | 57 | 57 |

## 25 Cells

## 27 Cells

## 49 Cells

## 57 Cells

## 61 Cells

## 63 Cells

## 67 Cells

## 73 Cells

## 75 Cells

## 79 Cells

## 81 Cells

## 87 Cells

## 93 Cells

## 99 Cells

## 105 Cells

## 109 Cells

## 111 Cells

## 113 Cells

## 117 Cells

## 119 Cells

## 123 Cells

## 125 Cells

## 129 Cells

## 147 Cells

## 213 Cells

## 225 Cells

## 267 Cells

## Unsolved

Last revised 2023-02-10.

Back to Polyform Oddities
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Polyform Curiosities

Col. George Sicherman
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