The Hexominoes
The hexominoes are, of course, polyominoes made from six squares. There are exactly 35 of them, and here they are (picture from Wikipedia):
They are color-coded by their symmetry - gray ones have no symmetry, red ones have one horizontal/vertical axis of symmetry, green ones have one diagonal axis of symmetry, blue ones have 180-degree rotational symmetry, and purple ones have two horizontal/vertical axes of symmetry. Since there are 35 of them giving each one a name is harder than for the lower pentominoes. There have been some attempts like this one:
As amusing as this is, it has some problems, mainly that a lot of it is rather arbitrary - for example the "M" hexomino if you rotate it could just as well be called a "W" hexomino, and vice versa, and the U hexomino in my opinion looks a lot like an F when you rotate it - the C hexomino can be called a U hexomino as well. As you can see there are a lot of problems with such a nomenclature. So for our purposes we'll instead number them, which is much less arbitrary:
With that designation, we're know ready to review each of the hexominoes, once again sorted by how they behave.
The Dying Hexominoes
4 die 4
5 die 4
10 die 5
12 die 6
18 die 6
21 die 4
22 die 9
23 die 3
24 die 4
26 die 7
27 die 7
35 die 5
1 die 12
30 die 15
28 die 45
The Still-Life Hexominoes
3 block 4
13 block 4
14 block 3
31 beehive 1
16 loaf 1
7 boat 2
17 boat 4
32 pond 3
34 aircraft carrier 1
The Oscillator Hexominoes
6 4Bli 9
2 2Bli 40
15 toad 0
The Four-Block Hexominoes
8 4Blo 64
9 4Blo 67
11 4Blo 67
20 4Blo 63
The Methuselah Hexominoes
29 8Blo 6G 4Bli 4Bh 1L 1Bo 1Sh 1102
19 3Blo 1Bli 103
33 6Blo 5Bli 2P 174
25 6Blo 5Bli 2P 179