Tiling a Badge with a Pentiamond and a Heptiamond

Introduction

A pentiamond is a plane figure formed by joining 5 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 pentiamond 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 smaller solutions.

See also:

  • Tiling a Triangle with a Pair of Polyiamonds

    • 22 Cells

    24 Cells

    33 Cells

    36 Cells

    37 Cells

    46 Cells

    54 Cells

    61 Cells

    69 Cells

    73 Cells

    78 Cells

    81 Cells

    88 Cells

    96 Cells

    100 Cells

    109 Cells

    117 Cells

    121 Cells

    132 Cells

    148 Cells

    150 Cells

    177 Cells

    198 Cells

    216 Cells

    249 Cells

    297 Cells

    384 Cells

    537 Cells

    708 Cells

    Last revised 2025-05-20.

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