Trihex-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.

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

See also Tetrahex-Pentahex Oddities and Pentahex Pair Oddities.

Johann Schwenke improved on one of my solutions.

Basic Solutions

3A+5A 373A+5C 673A+5D 313A+5E 613A+5F 31
3A+5H 313A+5I 373A+5J 373A+5K 553A+5L 37
3A+5N 193A+5P 313A+5Q 733A+5R 553A+5S 61
3A+5T 733A+5U 493A+5V 373A+5W 673A+5X 25
3A+5Y 253A+5Z 553I+5A 313I+5C 613I+5D 19
3I+5E 133I+5F 313I+5H 553I+5I 313I+5J 19
3I+5K 373I+5L 193I+5N 373I+5P 373I+5Q 43
3I+5R 373I+5S 613I+5T 313I+5U 193I+5V 19
3I+5W 313I+5X 493I+5Y 373I+5Z 493V+5A 31
3V+5C 313V+5D 313V+5E 373V+5F 313V+5H 25
3V+5I 433V+5J 193V+5K 313V+5L 313V+5N 19
3V+5P 193V+5Q 313V+5R 313V+5S 373V+5T 37
3V+5U 313V+5V 313V+5W 253V+5X 313V+5Y 37
3V+5Z 25

Holeless Variants

Solutions shown above that are holeless are not shown here.

3A+5C —3A+5Q —3A+5T 793A+5U 853A+5W 73
3I+5A 373I+5F 553I+5Q 613I+5Z 553V+5H 31
3V+5L 373V+5U 373V+5W 31

Last revised 2021-07-26.

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