Kristie - I can't see how to paper piece this one and avoid the Y seams. I'd love to see how you managed this one.
One again, our starting components...
This one starts off with 5 square in a square blocks. I also pieced the outer rectangles and the middle pieces to make the lovely trapezoids.
Now for the Y seams... Mark the corners of the centre square in a square block and all 4 trapezoids. For the trapezoids, you only need to make the 2 corners of the narrow side. The pencil marks are a little faint but I think you can see them in the picture below.
Find and pin to those 1/4" marks. I also pined the centres for good measure. You want to sew only to the 1/4" seam allowance. Remember to back stitch on these seams. (Otherwise your block will unravel.)
Once you've completed all 4 sides, you'll have this funny looking block with the diagonal seams still to go. (The observant among you will notice that my block is very un-square like. I remembered to cut the parallelograms wider than the pattern called for but forgot the triangles.) I recommend cutting the two a little wider than called for and trimming the square down when you're done. (The blue fabric is there just to show the un-sewn seam)
Fold your block and pin your Y seams. Once again, only sew to your 1/4" seam allowance and remember to backstitch. Once you've done this for all 4 seams, press and square up your block.
We're now back to our friend the 9-patch. Isn't it interesting that we can send up with so many different blocks with the same basic elements. This makes me think of all sorts of math related analogies, but I'll spare you. :)