Tetrahex-Pentahex Oddities


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 and Pentahex Pair Oddities.

Basic Solutions

4I+5A 854I+5C 2114I+5D 374I+5E 614I+5F 85
4I+5H 1514I+5I 254I+5J 794I+5K 854I+5L 49
4I+5N 374I+5P 374I+5Q 854I+5R 614I+5S 121
4I+5T 1874I+5U 1634I+5V 614I+5W 1454I+5X 127
4I+5Y 374I+5Z 854J+5A 374J+5C 374J+5D 37
4J+5E 374J+5F 374J+5H 374J+5I 494J+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 734O+5T 79
4O+5U 1574O+5V 194O+5W 434O+5X 734O+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 109
4S+5J 554S+5K 254S+5L 614S+5N 314S+5P 25
4S+5Q 674S+5R 314S+5S 734S+5T 974S+5U 67
4S+5V 1094S+5W 554S+5X 734S+5Y 554S+5Z 55
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 1634Y+5F 854Y+5H 614Y+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 1094Y+5X 314Y+5Y 914Y+5Z 109

Holeless Variants

Solutions shown above that are holeless are not shown here.

4I+5C 2414I+5F 1214I+5H 1574I+5J 854I+5L 61
4I+5S 1694I+5T 2714I+5U —4I+5W 1514O+5J 85
4O+5U —4S+5C —4S+5J 854S+5K 554S+5P 31
4S+5Q —4S+5T —4U+5C 1154U+5E 914U+5F 55
4U+5J 1154U+5K 554U+5N 554U+5Q 674U+5R 73
4U+5S 1094U+5T 1574U+5U 734U+5V 1034U+5X 73
4U+5Y 614U+5Z 734Y+5A 2054Y+5C —4Y+5E 217
4Y+5F 1154Y+5H 1694Y+5I —4Y+5K 914Y+5L 121
4Y+5Q 1214Y+5R 1334Y+5S —4Y+5T 314Y+5U 115
4Y+5V 974Y+5W 2054Y+5Z 133

Last revised 2020-01-28.

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Col. George Sicherman [ HOME | MAIL ]