# Yin/Yang Pentahexes

## Introduction

A pentahex is a polyform made by joining five equal regular hexagons edge to edge. There are 22 pentahexes, ignoring rotations and reflections.

The Yin/Yang problem is to find a holeless polyhex that can be tiled by each of two different pentahexes, leaving a single hole shaped like the other. It was inspired by the corresponding problem of Jenard Cabilao for pentominoes, which you may see (in Flemish) at KSO Glorieux's Pentomino site.

Here I show minimal known Yin/Yang solutions for every pair of pentahexes. If you find a smaller solution or solve an unsolved case, please write.

## Key

I use Erich Friedman's nomenclature for pentahexes:

## Solutions

5A-5C5A-5D5A-5E5A-5F5A-5H5A-5I
5A-5J5A-5K5A-5L5A-5N5A-5P5A-5Q
5A-5R5A-5S5A-5T5A-5U5A-5V
5A-5W5A-5X5A-5Y5A-5Z
5C-5D5C-5E5C-5F5C-5H5C-5I
5C-5J5C-5K5C-5L5C-5N5C-5P5C-5Q
5C-5R5C-5S5C-5T5C-5U5C-5V5C-5W
5C-5X5C-5Y5C-5Z5D-5E5D-5F5D-5H
5D-5I5D-5J5D-5K5D-5L5D-5N5D-5P
5D-5Q5D-5R5D-5S5D-5T5D-5U5D-5V
5D-5W5D-5X5D-5Y5D-5Z5E-5F5E-5H
5E-5I5E-5J5E-5K5E-5L5E-5N5E-5P
5E-5Q5E-5R5E-5S5E-5T5E-5U5E-5V
5E-5W5E-5X5E-5Y5E-5Z5F-5H5F-5I
5F-5J5F-5K5F-5L5F-5N5F-5P5F-5Q
5F-5R5F-5S5F-5T5F-5U5F-5V5F-5W
5F-5X5F-5Y5F-5Z5H-5I5H-5J5H-5K
5H-5L5H-5N5H-5P5H-5Q5H-5R5H-5S
5H-5T5H-5U5H-5V5H-5W5H-5X5H-5Y
5H-5Z5I-5J5I-5K5I-5L5I-5N5I-5P
5I-5Q5I-5R5I-5S5I-5T5I-5U
5I-5V5I-5W5I-5X5I-5Y5I-5Z5J-5K
5J-5L5J-5N5J-5P5J-5Q5J-5R5J-5S
5J-5T5J-5U5J-5V5J-5W5J-5X5J-5Y
5J-5Z5K-5L5K-5N5K-5P5K-5Q5K-5R
5K-5S5K-5T5K-5U5K-5V5K-5W5K-5X
5K-5Y5K-5Z5L-5N5L-5P5L-5Q5L-5R
5L-5S5L-5T5L-5U5L-5V5L-5W5L-5X
5L-5Y5L-5Z5N-5P5N-5Q5N-5R5N-5S
5N-5T5N-5U5N-5V5N-5W5N-5X5N-5Y
5N-5Z5P-5Q5P-5R5P-5S5P-5T5P-5U
5P-5V5P-5W5P-5X5P-5Y5P-5Z5Q-5R
5Q-5S5Q-5T5Q-5U5Q-5V5Q-5W5Q-5X
5Q-5Y5Q-5Z5R-5S5R-5T5R-5U5R-5V
5R-5W5R-5X5R-5Y5R-5Z5S-5T5S-5U
5S-5V5S-5W5S-5X5S-5Y5S-5Z5T-5U
5T-5V5T-5W5T-5X5T-5Y5T-5Z5U-5V
5U-5W5U-5X5U-5Y5U-5Z5V-5W5V-5X
5V-5Y5V-5Z5W-5X5W-5Y5W-5Z5X-5Y
5X-5Z5Y-5Z

Last revised 2013-08-01.

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Col. George Sicherman [ HOME | MAIL ]