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Welcome to the PolyominoesTiling project! This wiki serves as a comprehensive guide to help you understand, contribute to, and make the most of this project. Whether you're a developer looking to contribute, a user seeking to understand the functionalities, or just someone interested in polyomino tiling, you're in the right place.
PolyominoesTiling is a JavaScript project that focuses on tiling areas using various shapes known as polyominoes and polycubes. A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge, while a polycube is a 3D analog formed by joining one or more equal cubes face to face. This project explores the fascinating world of polyominoes and polycubes, their properties, and their applications in tiling and problem-solving.
To get started with PolyominoesTiling, you'll need a basic understanding of JavaScript and familiarity with concepts related to polyominoes and polycubes. This section will guide you through the initial steps to set up the project on your local machine.
Polyominoes are plane geometric figures formed by joining one or more equal squares edge to edge. They are a type of polyform, a geometric figure formed by joining together identical basic shapes. The most common polyominoes are:
| n | name | free | one-sided | fixed | total | with holes | without holes |
|---|---|---|---|---|---|---|---|
| 1 | monomino | 1 | 0 | 1 | 1 | 1 | 1 |
| 2 | domino | 1 | 0 | 1 | 1 | 1 | 2 |
| 3 | tromino | 2 | 0 | 2 | 2 | 2 | 6 |
| 4 | tetromino | 5 | 0 | 5 | 7 | 7 | 19 |
| 5 | pentomino | 12 | 0 | 12 | 18 | 18 | 63 |
| 6 | hexomino | 35 | 0 | 35 | 60 | 60 | 216 |
| 7 | heptomino | 108 | 1 | 107 | 196 | 196 | 760 |
| 8 | octomino | 369 | 6 | 363 | 704 | 704 | 2,725 |
| 9 | nonomino | 1,285 | 37 | 1,248 | 2,500 | 2,500 | 9,910 |
| 10 | decomino | 4,655 | 195 | 4,460 | 9,189 | 9,189 | 36,446 |
| 11 | undecomino | 17,073 | 979 | 16,094 | 33,896 | 33,896 | 135,268 |
| 12 | dodecomino | 63,600 | 4,663 | 58,937 | 126,759 | 126,759 | 505,861 |
Example:
- Tetrominoes: These include shapes like the "I", "O", "T", "S", and "Z" shapes found in Tetris.
- Pentominoes: There are 12 distinct pentominoes, each named after letters they resemble, such as "F", "I", "L", "P", and "T".
Polycubes are three-dimensional analogs of polyominoes, formed by joining one or more equal cubes face to face. Here are some common polycubes:
| n | name | free | one-sided | fixed | total | with holes | without holes |
|---|---|---|---|---|---|---|---|
| 1 | monocube | 1 | 0 | 1 | 1 | 1 | 1 |
| 2 | dicube | 1 | 0 | 1 | 1 | 1 | 1 |
| 3 | tricube | 2 | 0 | 2 | 3 | 3 | 3 |
| 4 | tetracube | 7 | 0 | 7 | 8 | 8 | 8 |
| 5 | pentacube | 29 | 1 | 28 | 34 | 34 | 34 |
| 6 | hexacube | 166 | 6 | 160 | 222 | 222 | 222 |
| 7 | heptacube | 1,019 | 33 | 986 | 1,515 | 1,515 | 1,515 |
Example:
- Tetracubes: These include shapes like the "L", "T", and "S" shapes, similar to their 2D counterparts but in 3D.
- Pentacubes: There are 29 distinct pentacubes, each with unique 3D shapes.
Tiling, or tessellation, is the process of covering a plane or space using one or more geometric shapes with no overlaps and no gaps. Tiling with polyominoes involves arranging these shapes in a way that completely covers a region, often a rectangle or other regular shapes. Similarly, tiling with polycubes involves covering a 3D volume.
PolyominoesTiling is open-source software licensed under the MIT License. For more information, see the License section.
If you have any questions or need further assistance, feel free to reach out to us through the project's GitHub repository.
Thank you for your interest in PolyominoesTiling!