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. | |
Polyomino Bireptiles. Join two copies of a polyomino, then dissect the result into equal smaller copies of it. | |
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. | |
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. | |
Polyiamond Bireptiles. Join two copies of a polyiamond, then dissect the result into equal smaller copies of it. |
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. | |
Polytan Bireptiles. Join two copies of a polytan, then dissect the result into equal smaller copies of it. | |
Scaled Polytan Tetrads. Join four similar polytans so that each borders the other three. | |
Similar Pentatan Figures 2–2√2–3√2. Arrange the 30 pentatans to make three copies of the same pentatan at scales 2, 2√2, and 3√2. |
Polydrafter Irreptiling. Tile a polydrafter with smaller copies of itself, not necessarily equal. | |
Polydrafter Bireptiles. Join two copies of a polydrafter, then dissect the result into equal smaller copies of it. |
Kiteless Didoms. Form shapes with the set of 12 didoms, omitting the kite didom. | |
Scaled Polydom Tetrads. Join four similar polydoms so that each borders the other three. |
Contiguous Reverse Partridge Tilings. Use 1 shape at scale n, 2 at scale n−1, and so on up to n at scale 1, to form a scaled copy of the shape in which equal tiles are contiguous. |
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. | |
Polycube Bireptiles. Join two copies of a polycube, then dissect the result into equal smaller copies of it. | |
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. | |
Pentacube Pair Pyramids. Join copies of two polycubes to make a pyramid. |