Edited - some comments may now be out-of-date.

I thought I had a complete set of solutions to this:

    Cut a square into indentical pieces so
    that they all touch the center point.

It became clear after some discussions that I was very, very wrong.

There are infinite familes of solutions, and a sporadic.  So I ahve
two questions:

1. What do you think is a complete set of solutions?

2. What techniques and approaches can I use to prove that the ones
I have are all there are?

Hope that's clearer. Thanks.