Tiling Regular Hexagons with Scaled Hexiamond Pairs

A hexiamond is a plane figure formed by joining six equal equilateral triangles edge to edge. There are 12 hexiamonds, independent of rotations and reflections:

A scaled hexiamond is a hexiamond that may be scaled up by an integer factor.

Here I show the fewest copies of two scalable hexiamonds that can tile some regular hexagon. If you find a smaller solution or solve an unsolved case, please write.

See also

  • Polyiamond Hexagon Tiling
  • Tiling a Regular Hexagon with a Scaled Pentiamond and Hexiamond
    •

    Table of Solutions

    This table shows the fewest tiles known to be able to tile a regular hexagon.

    AEFHILOPSUVX
    A * 21 4 18 9 4 14 21 28 7 18 25
    E 21 * 12 — 12 7 4 22 — 9 16 —
    F 4 12 * 13 8 4 13 10 15 9 10 15
    H 18 — 13 * 12 9 9 22 — 4 7 —
    I 9 12 8 12 * 7 8 9 12 12 9 13
    L 4 7 4 9 7 * 4 7 24 4 7 15
    O 14 4 13 9 8 4 * 9 — 25 4 13
    P 21 22 10 22 9 7 9 * 9 9 4 15
    S 28 — 15 — 12 24 — 9 * 9 12 —
    U 7 9 9 4 12 4 25 9 9 * 12 46
    V 18 16 10 7 9 7 4 4 12 12 * 4
    X 25 — 15 — 13 15 13 15 — 46 4 *

    4 Tiles

    7 Tiles

    8 Tiles

    9 Tiles

    10 Tiles

    12 Tiles

    13 Tiles

    14 Tiles

    15 Tiles

    16 Tiles

    18 Tiles

    21 Tiles

    22 Tiles

    24 Tiles

    25 Tiles

    28 Tiles

    46 Tiles

    Last revised 2025-03-30.

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    Col. George Sicherman [ HOME | MAIL ]