Tetrahex-Pentahex Oddities

Introduction

A polyhex oddity is a symmetrical figure formed by an odd number of copies of a polyhex. Symmetrical figures can also be formed with copies of two different polyhexes. Since a tetrahex has 4 cells and pentahex has 5, I use an odd number of cells rather than an odd number of tiles.

Here are the smallest known fully symmetric polyhexes with an odd number of cells, formed by copies of a given tetrahex and pentahex, using at least one of each.

See also Tetromino-Pentomino Oddities, Pentomino Pair Oddities, Hexiamond Pair Oddities, Pentahex Pair Oddities, and Trihex-Pentahex Oddities.

Johann Christoph Schwenke improved on some of my solutions.

Chronology of Solutions

[CHRONOLOGY]

Basic Solutions

4I+5A 854I+5C 1754I+5D 374I+5E 614I+5F 85
4I+5H 1094I+5I 254I+5J 794I+5K 854I+5L 49
4I+5N 374I+5P 374I+5Q 854I+5R 614I+5S 121
4I+5T 1094I+5U 1214I+5V 614I+5W 1454I+5X 121
4I+5Y 374I+5Z 854J+5A 374J+5C 374J+5D 37
4J+5E 374J+5F 374J+5H 374J+5I 374J+5J 37
4J+5K 374J+5L 374J+5N 374J+5P 374J+5Q 37
4J+5R 374J+5S 374J+5T 374J+5U 374J+5V 37
4J+5W 374J+5X 374J+5Y 374J+5Z 374O+5A 91
4O+5C 554O+5D 314O+5E 614O+5F 554O+5H 55
4O+5I 614O+5J 674O+5K 554O+5L 374O+5N 61
4O+5P 314O+5Q 314O+5R 614O+5S 674O+5T 79
4O+5U 1274O+5V 194O+5W 434O+5X 674O+5Y 61
4O+5Z 554Q+5A 374Q+5C 254Q+5D 314Q+5E 25
4Q+5F 314Q+5H 314Q+5I 374Q+5J 374Q+5K 25
4Q+5L 374Q+5N 194Q+5P 194Q+5Q 134Q+5R 31
4Q+5S 134Q+5T 134Q+5U 374Q+5V 374Q+5W 37
4Q+5X 374Q+5Y 374Q+5Z 374S+5A 854S+5C 97
4S+5D 314S+5E 734S+5F 254S+5H 554S+5I 103
4S+5J 554S+5K 254S+5L 614S+5N 314S+5P 25
4S+5Q 674S+5R 314S+5S 734S+5T 734S+5U 67
4S+5V 1094S+5W 554S+5X 734S+5Y 554S+5Z 49
4U+5A 134U+5C 554U+5D 374U+5E 494U+5F 49
4U+5H 494U+5I 134U+5J 254U+5K 494U+5L 37
4U+5N 494U+5P 314U+5Q 614U+5R 554U+5S 49
4U+5T 674U+5U 554U+5V 854U+5W 854U+5X 49
4U+5Y 494U+5Z 494Y+5A 1094Y+5C 1334Y+5D 79
4Y+5E 1454Y+5F 854Y+5H 554Y+5I 1754Y+5J 19
4Y+5K 494Y+5L 794Y+5N 194Y+5P 194Y+5Q 37
4Y+5R 794Y+5S 1574Y+5T 254Y+5U 494Y+5V 31
4Y+5W 1034Y+5X 314Y+5Y 914Y+5Z 109

Holeless Variants

Solutions shown above that are holeless are not shown here.

4I+5C 2174I+5F 1214I+5J 854I+5L 614I+5S 169
4I+5T 1754I+5U 2654I+5W 1514O+5J 854O+5U 283
4S+5C —4S+5I 1094S+5J 854S+5K 554S+5P 31
4S+5Q —4S+5T —4S+5Z 554U+5C 1154U+5E 91
4U+5F 554U+5J 1154U+5K 554U+5N 554U+5Q 67
4U+5R 734U+5S 1094U+5T 1574U+5U 734U+5V 103
4U+5X 734U+5Y 614U+5Z 734Y+5A 2054Y+5C —
4Y+5E 2174Y+5F 1154Y+5I —4Y+5K 914Y+5L 121
4Y+5Q 1214Y+5R 1214Y+5S —4Y+5T 314Y+5U 115
4Y+5V 974Y+5W 151

Last revised 2021-08-19.


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Col. George Sicherman [ HOME | MAIL ]