Out of main block fabric, cut four squares 3" x 3".
Out of background fabric, cut four squares 3" x 3".
With a pencil or marker, draw a diagonal line corner to corner on the wrong side of all four background fabric squares.
Pair up each background fabric square with a main fabric square and place them right sides together. Sew a seam 1/4" from the diagonal line on each side of the line.
Cut on the diagonal line. Press open.
You will now have eight half square triangles. Lay them out as in the photo below.
Sew them together to form two pinwheel blocks.
Cut out a 1" square from the center of one of the pinwheel blocks to reduce bulk.
Trace or print the center shape of the block onto the dull side of freezer paper and cut out. Iron this shape onto the right side of one of the pinwheel blocks, carefully lining up the seam lines on the shape with the actual seams on the block.
Cut out, leaving a seam allowance of about 1/4".
Place the shape section right side up onto the right side of the pinwheel block, lining up all the seam lines.
Baste through all layers. (I forgot to take a photo here.)
Turning the seam allowance under, applique the shape to the block.
Trim the resulting block to 3 5/8" square.
Out of background fabric, cut two squares 3 1/8" x 3 1/8" and cut each in half on the diagonal.
Sew the background fabric triangles to the center section as below. Sew opposing triangles first and then the remaining two.
Use your preferred applique method to applique the diamond shapes to the block.