POLYOMINO TILINGS

Polyomino Tilings

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L2 15-omino

Area: 15.

Perimeter: 20.

Size: 3x7.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 60.

Square order: 60.

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle and smallest square (30x30):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h1-293031-4445N>0
1-290
30022P
31-44000
4500000
4600000?
4700000?
4800000?
4900000?
5000000?
5100000?
5200000?
5300000?
5400000?
5500000?
5600000?
5700000?
5800000?
5900000?
60044C000?
61000???
62000???
63000???
64000???
65000???
66000???
67000???
68000???
69000???
70000???
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89000???
90088C0???
91000???
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100000???
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12001616C0???
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143000???
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146000???
147000???
148000???
149000???
15003232C0???
N>0x30kx?

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²12²13²14²15²16²
L2 15-omino1000000000000000

Attributions

  1. 30x30 rectangle was first found by William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192 (https://www.sciencedirect.com/science/article/pii/S0097316597927308).

See Also

O1 12-ominoDominoes