Two-Pentomino Balanced Rectangles. Tile a rectangle with two pentominoes in equal quantities. | |
Two-Pentomino Holey Balanced Rectangles. Tile a rectangle with two pentominoes in equal quantities, allowing one-cell holes. | |
Scaled Two-Pentomino Rectangles. Tile a rectangle with two pentominoes at various sizes. | |
Scaled Two-Pentomino Balanced Rectangles. Tile a rectangle with various sizes of two pentominoes in equal areas. | |
Scaled Three-Pentomino Rectangles. Tile a rectangle with three pentominoes at various sizes. | |
Three-Pentomino Balanced Rectangles. Tile a rectangle with three pentominoes in equal quantities. | |
Scaled Three-Pentomino Balanced Rectangles. Tile a rectangle with various sizes of three pentominoes in equal areas. | |
L Shapes From Two Pentominoes. Form an L-shaped (hexagonal) polyomino with copies of two pentominoes, using at least one of each. | |
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. | |
Covering a Rectangle with Copies of a Polyomino. Find the largest rectangles that copies of a polyomino can cover without overlapping. | |
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. | |
Tiling a Polyhex with the 12 Hexiamonds. Arrange the 12 hexiamonds to form a polyhex. | |
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. | |
Convex Polygons from Three Hexiamonds. With copies of three given hexiamonds make the smallest convex polyiamond. | |
Polyiamond Bireptiles. Join two copies of a polyiamond, then dissect the result into equal smaller copies of it. | |
Containing Pairs of Hexiamonds. Find the smallest polyiamonds that can contain every pair of distinct hexiamonds. | |
Tiling a Shape with Ternary Symmetry with the Heptiamonds and the Tetrahexes. Tile a shape with 3-fold symmetry with all 24 heptiamonds, then with all 7 tetrahexes. | |
The Lobster and the Snake. Four puzzles about the Lobster and Snake hexiamonds. |
Polyabolo Irreptiles. Join variously sized copies of a polyabolo to make a replica of itself. | |
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 a Right Trapezoidal Triabolo. Join variously sized copies of a polyabolo to make a right trapezoidal triabolo. | |
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. | |
Similar Polyaboloes Tiling a Crown Heptabolo. Join variously sized copies of a polyabolo to make a crown heptabolo. | |
Similar Polyaboloes Forming a Convex Shape. Join variously sized copies of a polyabolo to make a convex shape. | |
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. | |
Tiling a Polytan With Unequal Monotans. Dissect an arbitrary polytan into isosceles right triangles, all of different sizes. | |
Polyfett Irreptiles. Tile a polyfett with smaller copies of itself, not necessarily equal. | |
Similar Polyfetts Tiling a Triangle. Tile a triangle with variously sized copies of a polyfett. | |
Similar Polyfetts Tiling a Square. Tile a square with variously sized copies of a polyfett. |
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. | |
The Didrafter Fish. Form a compact shape with the 13 proper and extended didrafters. | |
Scaled Polydrafter Tetrads. Join four similar polydrafters so that each borders the other three. | |
Convex Figures with Didrafter Pairs. Make a convex polydrafter with copies of two didrafters. | |
Convex Figures with Didrafter Triplets. Make a convex polydrafter with copies of three didrafters. | |
Convex Shapes from the 13 Didrafters. Make a convex polydrafter with the 13 didrafters. | |
Rectangles Tiled with Three Didrafters. Make a rectangle with copies of three didrafters. | |
Regular Hexagons Tiled with Three Didrafters. Make a regular hexagon with copies of three didrafters. | |
Making a Rectangle from Different Didrafters. Make a rectangle out of up to eight distinct didrafters. | |
Didrafters at Scales 1 and 5. Arrange a double set of the 13 didrafters to form copies of a didrafter at scales 1 and 5. | |
Inflated Didrafters. Form a convex shape with the 13 didrafters after expanding some at integer scales or scales of an integer times √3. | |
Convex Figures with Tridrafter Pairs. Make a convex shape with copies of two tridrafters. | |
Galaxies from the 14 Tridrafters. Join the 14 proper tridrafters to make a shape with 6-rotary symmetry. | |
Stelo Twins and Triplets. Use Jacques Ferroul's Stelo pieces to make multiple copies of the same shape. |
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. | |
A Counterexample To
Livio Zucca's Island Conjecture.
Make a polydom islandin the shape of a polyomino that cannot be tiled with dominoes. | |
Convex Figures with Didom Pairs. Make a convex polydom with copies of two didoms. | |
Convex Figures with Didom Triplets. Make a convex polydom with copies of three didoms. | |
Convex Shapes from the 13 Didoms. Make a convex polydom with the 13 didoms, including the Kite Didom. | |
Inflated Didoms. Make a convex polydom with the 13 didoms, including the Kite Didom, enlarging some. | |
Tiling the Owen Dodecagon With Three Didoms. Make an almost regular dodecagon with copies of the 13 didoms. |
Contiguous Partridge Tilings. Use 1 shape at scale 1, 2 at scale 2, and so on up to n at scale n, to form a scaled copy of the shape in which equal tiles are contiguous. | |
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. | |
Lovebirds Tilings. Use 2 copies of a shape at scale 1, 4 at scale 2, and so on up to 2n at scale n, to form two scaled copies of the shape. |
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. | |
Filling Space with the Pansymmetric Heptacube. Use the 3D analogue of an X pentomino to fill space. | |
Tiling a Scaled Pentacube with a Pentacube. Use a pentacube to tile various pentacubes scaled up by 2 or 3. | |
Inflated Pentacubes. Make a box with the 29 pentacubes, enlarging one of them by a scale factor of 2. |