Tetracairo Compatibility

  • Introduction
  • Enumeration
  • Table
  • Solutions

    • Introduction

    A tetracairo is a polycairo with four cells. Two polyforms are compatible if there is a polyform that both of them can tile.

    Here I show minimal known compatibilities for pairs of tetracairos.

    Enumeration

    There are 17 tetracairos. They are shown below.

    Table

    This table shows the fewest tiles known to be needed for compatibility of two tetracairos.

    1234567891011121314151617
    1 * 4 4 2 2 4 2 4 × × 4 4 2 4 × 2 ×
    2 4 * 4 2 × 4 × 4 4 × 4 4 4 × × 4 ×
    3 4 4 * 4 4 4 4 2 2 × 4 4 4 × × × ×
    4 2 2 4 * 2 4 4 4 × × 4 4 2 4 × × ×
    5 2 × 4 2 * 4 × 4 × × 4 4 2 × × × ×
    6 4 4 4 4 4 * 4 4 4 × 4 4 4 2 × 4 4
    7 2 × 4 4 × 4 * 4 12 × 4 4 2 4 × 2 ×
    8 4 4 2 4 4 4 4 * 2 × 4 4 4 4 × × 4
    9 × 4 2 × × 4 12 2 * × 4 16 16 2 12 12 4
    10 × × × × × × × × × * 2 2 2 × × × ×
    11 4 4 4 4 4 4 4 4 4 2 * 2 2 4 4 4 ×
    12 4 4 4 4 4 4 4 4 16 2 2 * 2 4 2 4 2
    13 2 4 4 2 2 4 2 4 16 2 2 2 * 4 2 4 ×
    14 4 × × 4 × 2 4 4 2 × 4 4 4 * 4 × ×
    15 × × × × × × × × 12 × 4 2 2 4 * 2 ×
    16 2 4 × × × 4 2 × 12 × 4 4 4 × 2 * ×
    17 × × × × × 4 × 4 4 × × 2 × × × × *

    Solutions

  • 2 Tiles
  • 4 Tiles
  • 12 Tiles
  • 16 Tiles

    • 2 Tiles

    4 Tiles

    12 Tiles

    16 Tiles

    Last revised 2023-08-09.

    Back to Pairwise Compatibility < Polyform Compatibility < Polyform Curiosities
    Col. George Sicherman [ HOME | MAIL ]