Polyomino (EntityTopic, 5)
From Hi.gher. Space
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* Monomino - one hypercube. | * Monomino - one hypercube. | ||
* Domino - two hypercubes. | * Domino - two hypercubes. | ||
| - | * | + | * Tromino - three hypercubes. |
| - | * | + | * Tetromino - four hypercubes. |
etc. | etc. | ||
Revision as of 23:06, 5 May 2009
A polyomino (also spelt polimino and polymino) is a collection of hypercubes joined so that one hypercell of one touches another hypercell of another. Polyominoes are named as follows:
- Monomino - one hypercube.
- Domino - two hypercubes.
- Tromino - three hypercubes.
- Tetromino - four hypercubes.
etc.
We can generalize sets of polyominoes as p(c,d) where c is the number of hypercubes and d is the number of dimensions.
In n dimensions, there are no new polyominoes that are not simply extrusions of n-1-dimensional polyominoes, if the number of hypercubes is equal to or less than the number of dimensions. In other words, p(c,d) = p(c,d-1) if d ≥ c.
Here is a table of the polyominoes available with various c and d:
http://teamikaria.com/dl/AajgNE5JwCjIPTn-3WsKyIUF4n6XpMuSpyTWuJ0ZYkjXiPUi.png
Octominoes
There are two special properties about octominoes:
- The first polyomino with a pocket is an octomino.
- The first polyomino with no linear symmetry, but rotational symmetry of order 4 is an octomino.
