Stacked (78) Chequered Solid (24) Domino Sliced (36) Diagonally Polarized (20) Solid (12) The Pentomino Family (by Peter F. Esser) Parallel Polarized (21) Same Chequered (24) Opposite Chequered (18) Parallel Magnetized (35) Diagonally Magnetized (34) One-sided (18) One-sided Polarized (35) One-sided Chequered (36) One-sided Magnetized (63) Corner-connected (12) One-sided Corner-connected (18) Pseudo (94) One-sided Truncated (35)

With the different attributes we get one to eight distinct copies for each piece. The table shows the numbers.

 Type X P I W T L V U N Y F Z Sum one-sided 1 2 1 1 1 2 1 1 2 2 2 2 18 parallel polarized 1 2 2 1 2 2 1 2 2 2 2 2 21 diagonally polarized 1 2 1 2 1 2 2 1 2 2 2 2 20 same chequered 2 2 2 2 2 2 2 2 2 2 2 2 24 opposite chequered 1 2 1 1 1 2 1 1 2 2 2 2 18 parallel magnetized 1 4 2 2 3 4 2 3 4 4 4 2 35 diagonally magnetized 1 4 1 3 2 4 3 2 4 4 4 2 34 one-sided chequered 2 4 2 2 2 4 2 2 4 4 4 4 36 one-sided polarized 1 4 2 2 2 4 2 2 4 4 4 4 35 one-sided magnetized 1 8 2 4 4 8 4 4 8 8 8 4 63

We can flip or rotate the simple pentominoes. If one or two of these operations isn't allowed, we get the special pieces. I like a physical arguments to allow or forbid the operations and chose these names. But it's also possible to choose special forms e.g. rectangular cells for the polarized pieces.

 Allowed Tranformations Type reflect at line parallel to grid reflect at line diagonal to grid rotate 90 degree rotate 180 degree one-sided no no yes yes parallel polarized yes no no yes diagonally polarized no yes no yes parallel magnetized yes no no no diagonally magnetized no yes no no one-sided polarized no no no yes one-sided magnetized no no no no

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