Polyominoes in Rectangles

The order of a polyomino is the smallest number of copies of it which tile a rectangle. The prime rectangles of a polyomino are those rectangles which can be tiled which cannot be tiled with smaller prime rectangles. For small polyominoes, we give the order and prime rectangles. Click on the dimensions for a picture of the tiling.

Triominoes

PolyominoOrderPrime Rectangles
2 3x2
9x5

Tetrominoes

PolyominoOrderPrime Rectangles
4 4x4
2 4x2
8x3

Pentominoes

PolyominoOrderPrime Rectangles
2 5x2
15x7
2 5x2
15x7
10 10x5
20x9, 30x9, 45x9, 55x9
14x10, 16x10, 23x10, 27x10
20x11, 30x11, 35x11, 45x11
50x12, 55x12, 60x12, 65x12, 70x12, 75x12, 80x12, 85x12, 90x12, 95x12
20x13, 30x13, 35x13, 45x13
15x14
15x15, 16x15, 17x15, 19x15, 21x15, 22x15, 23x15
20x17, 25x17
25x18, 35x18
25x22

Hexominoes

PolyominoOrderPrime Rectangles
2 4x3
2 4x3
2 4x3
4 6x4
12x5
?
2 6x2
4x3
18x5
11x6
10x9
2 6x2
12x7
15x8
14x9, 16x9, 34x9
15x10
18x11
18 12x9, 20x9, 28x9
13x12, 14x12, 17x12, 19x12, 21x12, 24x12, 25x12, 29x12
24x13
28x15, 32x15, 36x15, 40x15, 44x15, 48x15, 52x15
18x16, 27x16, 30x16, 33x16, 39x16, 42x16
21x20, 24x20
?
92 24x23
29x24, 35x24, 41x24, 47x24, 53x24, 59x24, 63x24, 65x24, 71x24, 77x24, 83x24
?