# Polyform Tiling

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
The tiling problem is to join copies of one or more polyforms to make a given polyform.

## Plane Tiling

 Two-Pentomino Balanced Rectangles. Tile a rectangle with two pentominoes in equal quantities. 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 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. 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. Tiling a Triangle with Similar Polyaboloes. Join variously sized copies of a polyabolo to make a triangle. Tiling an Octagon with Similar Polyaboloes. Join variously sized copies of a polyabolo to make an octagon. Tiling a Home Plate Hexabolo with Similar Polyaboloes. Join variously sized copies of a polyabolo to make a home plate. 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. Similar Hexiamond Figures, 2–2–8. With the 12 hexiamonds, make three similar figures, one at double scale.

## Solid Tiling

 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. 33 + 43 + 53 = 63. 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.

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Col. George Sicherman [ HOME | MAIL ]