Tiling a Badge with a Pair of Polyiamonds

Introduction

A polyiamond is a plane figure formed by joining 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 two polyiamonds, using at least one of each. If you find a smaller solution, please write.

Carl Schwenke and Johann Schwenke contributed smaller solutions.

See also:

  • Tiling a Triangle with a Pair of Polyiamonds
  • Navigation

  • Triamond and Tetriamond
  • Tetriamond and Tetriamond
  • Triamond and Pentiamond
  • Tetriamond and Pentiamond
  • Pentiamond and Pentiamond
  • Triamond and Hexiamond
  • Tetriamond and Hexiamond
  • Pentiamond and Hexiamond
  • Hexiamond and Hexiamond
  • Triamond and Heptiamond
  • Tetriamond and Heptiamond
  • Pentiamond and Heptiamond
  • Hexiamond and Heptiamond
  • Heptiamond and Heptiamond
  • Triamond and Tetriamond

    13 Cells

    Tetriamond and Tetriamond

    16 Cells

    24 Cells

    36 Cells

    Triamond and Pentiamond

    13 Cells

    16 Cells

    Tetriamond and Pentiamond

    9 Cells

    13 Cells

    24 Cells

    33 Cells

    37 Cells

    46 Cells

    54 Cells

    73 Cells

    Pentiamond and Pentiamond

    25 Cells

    100 Cells

    150 Cells

    Triamond and Hexiamond

    9 Cells

    24 Cells

    33 Cells

    Tetriamond and Hexiamond

    16 Cells

    22 Cells

    24 Cells

    36 Cells

    52 Cells

    54 Cells

    64 Cells

    96 Cells

    Pentiamond and Hexiamond

    16 Cells

    22 Cells

    33 Cells

    37 Cells

    46 Cells

    52 Cells

    54 Cells

    61 Cells

    96 Cells

    157 Cells

    253 Cells

    286 Cells

    384 Cells

    Hexiamond and Hexiamond

    24 Cells

    36 Cells

    54 Cells

    96 Cells

    132 Cells

    144 Cells

    150 Cells

    216 Cells

    384 Cells

    486 Cells

    Triamond and Heptiamond

    13 Cells

    16 Cells

    22 Cells

    25 Cells

    Tetriamond and Heptiamond

    22 Cells

    25 Cells

    33 Cells

    37 Cells

    52 Cells

    54 Cells

    69 Cells

    88 Cells

    94 Cells

    96 Cells

    121 Cells

    208 Cells

    216 Cells

    864 Cells

    Last revised 2025-05-20.


    Back to Polyiamond and Polyming Tiling < Polyform Tiling < Polyform Curiosities
    Col. George Sicherman [ HOME | MAIL ]