Heptahex Oddities

A heptahex oddity is a figure with binary symmetry formed by an odd number of copies of a heptahex. Here are the minimal known oddities for heptahexes. Please write if you find a smaller solution or solve an unsolved case. Mike Reid contributed improvements to some of these solutions.

For hexahexes, see Hexahex Oddities. For other orders of polyhexes, see Trihex Oddities, Tetrahex Oddities, Pentahex Oddities, and Hexahex Oddities.

[ Rowwise Bilateral | Columnwise Bilateral | Birotary | Double Bilateral | Sextuple Rotary | Full ]

Rowwise Bilateral

1 to 15 tiles

17 to 27 tiles

33 or more tiles

Unsolved

Impossible

Columnwise Bilateral

1 to 7 tiles

9 to 11 tiles

13 to 21 tiles

27 or more tiles

Unsolved

Birotary

1 to 21 tiles

23 or more tiles

Double Bilateral

Sextuple Rotary

Full

For heptahex tilings of straight and ragged regular hexagons, see Tiling a Hexagon Polyhex with a Heptahex.

Holeless Variants

Last revised 2025-01-13.


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Col. George Sicherman [ HOME | MAIL ]