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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