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

Polyomino	Order	Prime Rectangles
	2	3x2 9x5

Tetrominoes

Polyomino	Order	Prime Rectangles
	4	4x4
	2	4x2 8x3

Pentominoes

Polyomino	Order	Prime 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

Polyomino	Order	Prime 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 ?