# Polyplet

A polyplet (or simply a plet) is a finite collection of orthogonally or diagonally connected cells. The form of connectivity allowed by polyplets is sometimes called king-wise connectivity because of the way a king moves on a chess board. King-wise connectivity is a more natural concept in Life-like cellular automata than the orthogonal connectivity of polyominoes.

## Sizes of polyplets

Polyplets with n cells for n = 3, 4, 5, ... are called triplets, tetraplets, pentaplets, hexaplets, heptaplets, and n-plets in general. The number of distinct polyplets with n cells for n = 1, 2, 3, ... is given by the sequence 1, 2, 5, 22, 94, 524, 3031, 18770, 118133, ... (Sloane's A030222).

### Triplets

There are exactly five distinct triplets, shown below. The first two are the two triominoes (pre-block and blinker), and the other three vanish after two generations (being the banana spark, V spark and a fuse of length 3 respectively).

The five distinct triplets.

### Tetraplets

Of the 22 distinct tetraplets:

The twenty-two distinct tetraplets.

### Pentaplets

The 94 distinct pentaplets evolve as follows:

• 39 into nothing
• 11 into loaves
• 10 into traffic lights
• 6 in the phase with "+" on even generations
• 4 in the phase with "o" on even generations
• 9 into beehives
• 7 into boats (including the boat itself)
• 4 into blocks
• 4 into gliders (including the two that are themselves phases of the glider)
• 3 into ponds
• 2 into tubs
• 1 into the pi heptomino (after two generations; the first generation evolution is the "<" hexomino)

The remaining four are or become the R-pentomino:

• one is the R-pentomino itself
• one becomes the R-pentomino after one generation
• two become the aforementioned pentaplet after one generation (and thus become the R-pentomino after two).

### Hexaplets

Lifeline Volume 4 analysed all six-cell patterns. Of the 524 that are polyplets, here are the results:

• 171 into nothing
• 38 into traffic lights
• 34 into loaves
• 33 into beehives (including the beehive itself)
• 30 into blocks
• 23 into honey farms
• 21 follow the pi-heptomino sequence
• 19 into boats
• 19 follow the lumps of muck sequence
• 17 into ponds
• 17 follow the R-pentomino sequence
• 10 follow the block and glider sequence
• 9 follow the century sequence
• 7 into ships (including the ship itself)
• 6 into barges (including the barge itself)
• 6 into beacons
• 5 follow the teardrop sequence
• 5 into gliders
• 5 follow the B-heptomino sequence
• 4 follow the I-heptomino sequence
• 3 into two asymmetric loaves
• 3 follow the two-glider octomino sequence
• 2 into the long boat, both shown on the long boat page
• 2 into the moth sequence[1]
• 1 (a hexomino) into aircraft carrier
• 1 (a hexomino) into two far blinkers
• 1 is the snake
• 1 is the clock
• 1 follows the butterfly sequence
• 1 follows the dove sequence
• 1 is a Herschel without the B's block
• 1 is the Iwona active region
• 1 is Thompson's methuselah (3o\$3bo\$3b2o!)

Tubs are absent from this list.

## References

1. David Raucci (April 4, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums