For a list of numbers of polyominoes up to order 28 see Tomás Oliveira e Silva's polyomino enumeration, Kevin L. Gong's The Mathematics of Polyominoes , Klarner's Lattice Animal Constant or Sloane's On-Line Encyclopedia of Integer Sequences (this also has links to symmetric polyomino numbers). For diagrams of polyominoes up to size 12 see Ambros Marzetta's List of polyominoes of order 4..12.
There is also some information in Polyominoes, etc. by Beeler, M., Gosper, R.W., and Schroeppel, R, Slavik Jablan's Polyominoes, Enumeration of Remarkable Families of Polyominoes by Dominique Gouyou-Beauchamps, Lawrence Detlor's Polypleura and Description des polyominos (in French).
To experiment with drawing some polyominoes try Phil's Polyomino Maker
For more technical information on the counting problem see A Procedure for Improving the Upper Bound for the Number of n-ominoes and A Finite Basis Theorem Revisited.
There are twelve pentominoes covering an area of 60 squares. This area can be made up with rectangles 2x30, 3x20 (2 solutions), 4x15 (368 solutions), 5x12 (1010 solutions) and 6x10 (2339 solutions). Since at least one of the pentominoes is of length 3 in two directions the 2x30 is not possible but all the others are (see below). The links above will show images of all solutions (some browsers may not be able to display the 2339 solutions of the 6x10).
The 5x12 and 6x10 rectangles can be made up of two 5x6 rectangles. There are eight solutions shown here.
Patrick Hamlyn has analysed the solutions of the various rectangles to determine which can be coloured with only three colours. He has found the following information on numbers of rectangles which can be three coloured. Strict colouring demands that no two identically coloured pieces touch even at a corner whereas non-strict colouring allows corner touching. No solution can be two coloured.
Three of the rectangles above can be coloured with three colours two with strict colouring - click here to see the image. As you can see from the numbers three coloured solutions can be quite rare with only 4% of the 6x10 rectangles having a strict three colouring. None of the rectangles will allow a two coloured solution. For the 4x15 rectangle there are just five essentially different ways to make a 4x5 and a 4x10 rectangle with the set. All these solutions can be three coloured.
To see a lists of solutions with diagrams go to Adrian Smith's Pentomino Relationships, Pentominos by Lars Kindermann, Eric Wassenaar's Introduction to Polyominoes or All Pentomino Solutions.
For just the 6x10 rectangle see also Wilfred J. Hansen's Equivalence Classes Among Pentomino Tilings of the 6x10 Rectangle
For an animation of the construction of a 3x20 rectangle see Michelle Raymond's Homepage or for animated solutions of all rectangles see Lars Kindermann's Pentominoes.
To try filling a 6 x 10 rectangle go to Robert's Neat Math Page - Pentominoes
Puzzlecraft sells a CD with a large number of pentomino problems.
Other sites with pentomino content are
Also Rudolfo Kurchan's Puzzle Fun has regular pentomino competitions.
You can see an octomino construction at Kadon Enterprises which sells sets of pieces.
David Bird has also made some constructions with octominoes and at least one with enneominoes. (These drawings have been supplied by Mike Reid)
Patrick Hamlyn has produced (by computer) a set of nine 7x47 rectangles each with a central hole with the octominoes.
Until 2005 only one enneomino pattern was known until Peter Esser produced five copies of the 17 x 137 rectangle below.
Peter Esser has noted that there are 1248 enneominoes if we omit the ones with holes and has produced a set of sixteen rectangles with the set.
Patrick Hamlyn has gone one stage better and produced 48 rectangles and believes that 96 might also be possible.
Peter has also produced this dekomino pattern.
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