Tiling a Badge with a Hexiamond and a Heptiamond

Introduction

A hexiamond is a plane figure formed by joining 6 equal equilateral triangles edge to edge. A heptiamond is a plane figure formed by joining 7 equal equilateral triangles edge to edge.

A polyiamond badge is a six-sided polyiamond whose alternate sides have equal length. It is a truncated equilateral triangle. A regular hexagon and an equilateral triangle are special cases of badges.

Here I show the smallest known badges that can be tiled by copies of a given hexiamond and heptiamond, using at least one of each. If you find a smaller solution or solve an unsolved case, please write.

Carl Schwenke and Johann Schwenke contributed new solutions and smaller solutions.

See also:

  • Tiling a Triangle with a Pair of Polyiamonds

    • 13 Cells

    25 Cells

    33 Cells

    37 Cells

    46 Cells

    49 Cells

    52 Cells

    54 Cells

    61 Cells

    64 Cells

    69 Cells

    73 Cells

    78 Cells

    81 Cells

    88 Cells

    94 Cells

    96 Cells

    100 Cells

    109 Cells

    117 Cells

    121 Cells

    132 Cells

    141 Cells

    148 Cells

    150 Cells

    177 Cells

    181 Cells

    198 Cells

    208 Cells

    214 Cells

    216 Cells

    249 Cells

    253 Cells

    276 Cells

    286 Cells

    292 Cells

    294 Cells

    297 Cells

    325 Cells

    333 Cells

    337 Cells

    384 Cells

    421 Cells

    528 Cells

    600 Cells

    726 Cells

    753 Cells

    1014 Cells

    2166 Cells

    4704 Cells

    Last revised 2025-08-11.

    Back to Tiling a Badge With a Pair of Polyiamonds < Polyiamond and Polyming Tiling < Polyform Tiling < Polyform Curiosities
    Col. George Sicherman [ HOME | MAIL ]