47. Magic Pento-square

In a magic square, the sum of the numbers in each row, column and
diagonal row is always the same.

We will start with the
most famous
magic square,
the Lo-Shu.

Lee Sallows had the brilliant idea to replace numbers by shapes. With all
shapes in any row, column or diagonal row the same main-shape must be
formed.

A magic 2010 !

Matthijs Coster from the Netherlands created a
competition for the
Dutch magazine Pythagoras.

We changed the question in that competition for our own pentomino-competition.

As shapes we choose the polyominoes.

In the figure below, you can see a magical square with shapes (or a
geo-magical square), of which one is a (red) F-pentomino.

Find 11 other geo-magical squares of size 3x3, using each of the other
11 pentominoes as a central piece once.

You have total freedom to decide on the main shape to be formed, as long
as each row and column contains a congruent shape.

The sizes of the 9 shapes must be 1 upto 9.