Edited - some comments may now be out-of-date.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:
What do you think is a complete set of solutions?
What techniques and approaches can I use to prove that the ones I have are all there are?
Hope that's clearer. Thanks.