Rep-tiles are figures which are dissected by the same figures as itself.
As you can see, the rep-tile of order 4 is also a rep-tile of order 9 in the above figures: Compare the L-shaped figure at row 2 column 1 and one at row 3 and column 1, and compare two trapezoids at row 1 and row 3.
As I know, Golomb found that a few rep-tiles of order 9 which are not of order 4. But, those examples are not simple closed curves.
So, my questions:
(1) Is any rep-tile of order 4 always of order 9?
(2) If a rep-tile of order 9 is a simple close curve, is it also of order 4?