Tiling a Hexagon Polyhex with a Heptahex

Introduction

A heptahex is a plane figure formed by joining 7 equal regular hexagons edge to edge. There are 333 heptahexes, not distinguishing reflections and rotations.

There are three kinds of regular hexagonal polyhexes:

Straight Sharp Ragged Blunt Ragged

Here I show the smallest hexagonal polyhex of each type that each heptahex can tile. If you find a smaller solution, or a solution for another heptahex, please write.

See also Heptahex Oddities. For equilateral triangular polyhexes, see Erich Friedman's Math Magic for March 2003.

  • Straight Hexagons
  • Sharp Ragged Hexagons
  • Blunt Ragged Hexagons
  • Nested Hexagons

    • Straight Hexagons

    1 Tile

    67 Tiles

    Some of these solutions were found by Mike Reid or Andrew Clarke or both.

    103 Tiles

    This solution was found by Carl Schwenke and Johann Schwenke.

    Sharp Ragged Hexagons

    49 Tiles

    Blunt Ragged Hexagons

    1 Tile

    79 Tiles

    Nested Hexagons

    Larger nests may be possible.

    Mike Reid discovered the orange and yellow layers of the 2nd nest.

    Last revised 2025-01-12.

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    Col. George Sicherman [ HOME | MAIL ]