Tiling a Hexagon Polyhex with a Pair of Heptahexes

Introduction

These seven heptahexes can tile a regular hexagon polyhex by themselves:

See Tiling a Hexagon Polyhex with a Heptahex for such tilings.

Edo Timmermans has asked which pairs of heptahexes can tile a regular hexagon polyhex, using at least one copy of each of the two heptahexes. There are 55,278 pairs of heptahexes. At Edo's suggestion, I exclude pairs in which at least one heptahex can tile a regular hexagon polyhex by itself. This leaves 52,975 pairs of heptahexes.

So far, I have found 306 such pairs that can tile a regular hexagon polyhex. I show some of these tilings below. If you find a pair of heptahexes with a larger minimal regular hexagon tiling, please write.

13 Tiles

31 Tiles

67 Tiles

Edo points out that the last tiling has one tile of each type surrounded by the other type.

Last revised 2025-02-13.