Polyomino (EntityTopic, 5)

From Hi.gher. Space

Revision as of 18:12, 1 December 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 hole is an octomino.
• The first polyomino with no linear symmetry, but rotational symmetry of order 4 is an octomino.