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. | |
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. | |
L Shapes from Pentacube Pairs. Join copies of two pentacubes to make an L-shaped prism. | |
L Shapes from the 29 Pentacubes. Join the 29 pentacubes to make an L-shaped 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. | |
Prisms with Square-Symmetric Bases from the 29 Pentacubes. Use all 29 pentacubes to form a prism whose base is a fully-symmetric 29-omino. |