 | 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. |
 | Three-Pentomino Holey Balanced Rectangles. Tile a rectangle with three pentominoes in equal quantities, allowing one-cell holes. |
 | 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. |
 | Similar Polyiamonds Forming a Convex Shape. Arrange scaled copies of a polyiamond to make a 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. |
 | Prime Boxes for the Clip Pentakedge. Identify the irreducible boxes that can be tiled by the Clip Pentakedge. |
 | Pentacubes in a Box Without Corners. Join copies of a pentacube to make a rectangular prism with its corner cells removed. |
 | Pentacubes in a Box With Four Edges Removed. Join copies of a pentacube to make a rectangular prism from which the cells along four parallel edges have been removed. |
 | Pentacubes in a Box With All Edges Removed. Join copies of a pentacube to make a rectangular prism from which the cells along the edges have been 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. |
 | 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. |
| 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. |