Symmetry Challenge

Christina from Marborough Primary, London has given this one some thought and made the sensible suggestion of trying to find all the symmetrical patterns with one coloured square, then with two squares, then three, then four. That's just what Tom has done below.

Tom was very careful in trying to make sure that he found them all. First, he looked for patterns with no coloured squares. Of course, there's only one of those:

Then he looked for patterns with one coloured square. Here are the patterns he found:

but that was the only one. Then he looked for patterns with this square coloured where the line of symmetry was horizontal, but he came up with the same one again (rotated, of course). Then he looked for ones where the line of symmetry was diagonal. Here are the two patterns he found:

These were the only symmetrical patterns with a corner square shaded. Next he shaded the top centre square and looked for patterns with a vertical line of symmetry. Here's what he found:

He noticed that he wouldn't get any new patterns by looking for ones with horizontal lines of symmetry, so he looked for patterns with a diagonal line of symmetry. This is the only one he found: