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, Pentahex Pair Oddities, and Trihex-Pentahex Oddities.

Johann Schwenke improved on some of my solutions.

Chronology of Solutions


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 794J+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 55
4O+5P 314O+5Q 314O+5R 614O+5S 674O+5T 79
4O+5U 1274O+5V 194O+5W 434O+5X 674O+5Y 55
4O+5Z 554Q+5A 314Q+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 674S+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 674S+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 614U+5W 794U+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 79

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+5N 61
4O+5U 2834O+5Y 614Q+5A 374S+5C —4S+5E 73
4S+5I 1094S+5J 854S+5K 554S+5P 314S+5Q —
4S+5T 1034S+5X 734S+5Z 554U+5C 1154U+5E 91
4U+5F 554U+5J 854U+5K 554U+5N 554U+5Q 67
4U+5R 734U+5S 1094U+5T 1334U+5U 734U+5V 103
4U+5W 854U+5X 734U+5Y 614U+5Z 734Y+5A 205
4Y+5C —4Y+5E 2174Y+5F 1154Y+5I —4Y+5K 91
4Y+5L 854Y+5Q 674Y+5R 1214Y+5S —4Y+5T 31
4Y+5U 1154Y+5V 974Y+5W 1334Y+5Z 109

Last revised 2023-01-19.

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Polyform Oddities < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]