Polyominoes | Polyiamonds | Polyhexes | Other Plane Polyforms | Solid Polyforms |
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Pentomino Compatibility. Given two pentominoes, construct a figure that can be tiled with either. | |

Vertical I-Pentomino Compatibility.
Given any polyomino, construct a figure that can be tiled
with it and with the I pentomino,
using the I pentomino only in vertical orientation. | |

Holeless Pentomino Odd Pairs. Holeless solutions for Livio Zucca's Pentomino Odd Pairs. | |

Pentomino Pair-Single Compatibility. Joint compatibility for two pentominoes with a third. | |

Holeless Hexomino Compatibility. Given two hexominoes, construct a holeless figure that can be tiled with either. | |

Tetromino-Pentomino Compatibility. Given a tetromino and a pentomino, construct a figure that can be tiled with either. | |

Holeless Tetromino-Hexomino Compatibility. Given a tetromino and a hexomino, construct a holeless figure that can be tiled with either. | |

Holeless Pentomino-Hexomino Compatibility. Given a pentomino and a hexomino, construct a holeless figure that can be tiled with either. | |

2×3 Hexomino Compatibility. Which polyominoes are compatible with the 2×3 rectangular hexomino? | |

Holey Heptomino Compatibility. Which polyominoes are compatible with the holey heptomino? | |

H Heptomino Compatibility. Which polyominoes are compatible with the H heptomino? | |

Voided Square Octomino Compatibility. Which polyominoes are compatible with the square octomino with a hole in it? | |

Pinwheel Octomino Compatibility. Which polyominoes are compatible with the pinwheel octomino? | |

Square Enneomino Compatibility. Which polyominoes are compatible with the square enneomino? | |

A Euphoric Heptomino. This heptominoes is compatible with every polyomino of order 6 or less. | |

Two Euphoric Octominoes. Two octominoes are compatible with every polyomino of order 6 or less. | |

Minimal Incompatibility for Polyominoes. What are the smallest polyominoes that are not compatible with a given polyomino? | |

Addendum to Polypolyominoes. New and smaller polyomino compatibilities for Giovanni Resta's Polypolyominoes. |

Pentiamond Compatibility. Given two pentiamonds, construct a figure that can be tiled with either. | |

Hexiamond Compatibility. Given two hexiamonds, construct a figure that can be tiled with either. | |

Heptiamond Compatibility. Given two heptiamonds, construct a figure that can be tiled with either. | |

Mixed Polyiamond Compatibility. Given two polyiamonds of different orders, construct a figure that can be tiled with either. | |

Hexagon Hexiamond Compatibility. Find a figure that can be tiled with a given polyiamond and with the Hexagon hexiamond. | |

Triangle Enneiamond Compatibility. Find a figure that can be tiled with a given polyiamond and with the triangular enneiamond. | |

Minimal Incompatibility for Polyiamonds. What are the smallest polyiamonds that are not compatible with a given polyiamond? |

Pentahex Compatibility. Given two pentahexes, construct a figure that can be tiled with either. | |

Pentahex Odd Pairs. Given two pentahexes, construct a figure that can be tiled with an odd number of either. | |

Mixed Polyhex Compatibility. Given two polyhexes of different sizes, find a polyhex that can be tiled with either. | |

Seven Euphoric Pentahexes. Each of these pentahexes is compatible with all 82 hexahexes. | |

Three Euphoric Hexahexes. Each of these hexahexes is compatible with all 82 hexahexes. | |

Ring Hexahex Compatibility. Which polyhexes are compatible with the ring hexahex? | |

Disk Heptahex Compatibility. Which polyhexes are compatible with the disk heptahex? | |

Minimal Incompatibility for Polyhexes. What are the smallest polyhexes that are not compatible with a given polyhex? |

Tripent-Tetrapent Compatibility. Figures that can be tiled by a given tripent and tetrapent. | |

Tripent-Pentapent Compatibility. Figures that can be tiled by a given tripent and pentapent. | |

Tetrapent-Pentapent Compatibility. Figures that can be tiled by a given tetrapent and pentapent. | |

Pentapent Compatibility. Figures that can be tiled by two different pentapents. | |

Tetrabolo Compatibility. Given two tetraboloes, construct a figure that can be tiled with either. | |

Pentabolo Compatibility. Given two pentaboloes, construct a figure that can be tiled with either. | |

Pentabolo Odd Pairs. Given two pentaboloes, construct a figure that can be tiled with an odd number of either. | |

Diabolo-Tetrabolo Compatibility. Given a diabolo and a tetrabolo, construct a figure that can be tiled with either. | |

Triabolo-Tetrabolo Compatibility. Given a triabolo and a tetrabolo, construct a figure that can be tiled with either. | |

Tetrabolo-Pentabolo Compatibility. Given a tetrabolo and a pentabolo, construct a figure that can be tiled with either. | |

Tetrahop Compatibility. Given two tetrahops, construct a figure that can be tiled with either. | |

Didrafter Compatibility. Given two didrafters, construct a figure that can be tiled with either. | |

Tetrakite Compatibility. Given two tetrakites, construct a figure that can be tiled with either. | |

Trigem Compatibility. Given two trigems, construct a figure that can be tiled with either. | |

Trihing Compatibility. Given two trihings, construct a figure that can be tiled with either. | |

Tetracairo Compatibility. Given two tetracairos, construct a figure that can be tiled with either. | |

Pentapenny Compatibility. Given two pentapennies, construct a figure that can be tiled with either. |

Tetracube Compatibility. Given two tetracubes, construct a figure that can be tiled with either. | |

Pentacube Compatibility. Given two pentacubes, construct a figure that can be tiled with either. | |

Pentacube Odd Pairs. Given two pentacubes, construct a figure that can be tiled with either, using an odd number of each. | |

Flat Hexacube Compatibility. Given two solid hexominoes, construct a figure that can be tiled with either. | |

Triominoid Compatibility. Given two triominoids, construct a figure that can be tiled with either. |

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Col. George Sicherman [ HOME | MAIL ]