The slabs
made a most intricate and fascinating design,
but a thoroughly unobtrusive one, unless one paid deliberate
attention to it.

—Carlos Castaneda,
*The Second Ring of Power*

Two-Pentomino Balanced Rectangles. Tile a rectangle with two pentominoes in equal quantities. | |

Scaled Two-Pentomino Balanced Rectangles. Tile a rectangle with various sizes of two pentominoes in equal areas. | |

Three-Pentomino Balanced Rectangles. Tile a rectangle with three pentominoes in equal quantities. | |

Prime Rectangle Tilings for the Y Pentomino. Irreducible rectangles formed of Y pentominoes. | |

Tiling a Beveled Rectangle with Polyominoes. | |

Yin-Yang Dominoes. Arrange 10 of the 12 pentominoes to cover a bi-colored domino. | |

Tiling Strips with Polyominoes. Tiling straight, bent, branched, and crossed infinite strips with polyominoes of orders 1 through 6. | |

Uniform Polyomino Stacks. Join copies of a polyomino to make a figure with uniform row width. | |

Perfect Polyominoes. Polyominoes that can be formed by joining all the smaller polyominoes that can tile them. | |

Prime Rectangles for Tetrakings.. For each tetraking, find the irreducible rectangles that it can tile. |

Two-Hexiamond Balanced Hexagons. Tile a regular hexagon with two hexiamonds in equal quantities. | |

Three-Hexiamond Balanced Hexagons. Tile a regular hexagon with three hexiamonds in equal quantities. | |

Polyiamond Hexagon Tiling. Tile a straight or ragged hexagon with various polyiamonds. | |

Hexiamond Triplets. Arrange the 12 hexiamonds to form three congruent polyiamonds. | |

Yin-Yang Diamonds. Arrange the 12 hexiamonds to cover a bi-colored diamond. | |

Similar Hexiamond Figures, 2–2–8. With the 12 hexiamonds, make three similar figures, one at double scale. | |

Minimal Convex Polyiamond Tilings. With copies of a given polyiamond make the smallest convex polyiamond. | |

Convex Polygons from Pairs of Polyiamonds. With copies of two given polyiamonds make the smallest convex polyiamond. |

Similar Polyaboloes Tiling a Triangle. Join variously sized copies of a polyabolo to make a triangle. | |

Similar Polyaboloes Tiling a Square. Join variously sized copies of a polyabolo to make a square. | |

Similar Polyaboloes Tiling an Octagon. Join variously sized copies of a polyabolo to make an octagon. | |

Similar Polyaboloes Tiling a Home Plate Hexabolo. Join variously sized copies of a polyabolo to make a home plate. | |

Convex Polygons from Pairs of Polytans. With copies of two given polytans make the smallest convex polytan. |

Polydrafter Irreptiling. Tile a polydrafter with smaller copies of itself, not necessarily equal. |

Bireptiles. Dissect two joined copies of a polyform into equal smaller copies. |

Pentacubes in a Box. Join copies of a pentacube to make a rectangular prism. | |

Pentacubes in a Box Without Corners. Join copies of a pentacube to make a rectangular prism with its corner cells removed. | |

Polycube Reptiles. Join copies of a polycube to make a larger copy of itself. | |

Proper Minimal Polycube Irreptiles. Join variously sized copies of a polycube to make a larger copy of itself, using fewer copies than would be needed if they were all the same size. | |

3^{3} + 4^{3}
+ 5^{3} = 6^{3}.
Dissect a cube of side 6 to make cubes of sides 3, 4, and 5. | |

Tiling a Solid Diamond Polycube With Right Tricubes. Dissect an octahedron-shaped polycube into L-shaped tricubes. | |

Symmetric Pentacube Triples. Join three different pentacubes to form a symmetric polycube. | |

Polycube Prisms. Join copies of a polycube to make a prism. |

Back to Polyform Curiosities

Col. George Sicherman [ HOME | MAIL ]