This project is using one of your new quilt squares.  I stitched a basting stitch around the design because I didn't have a complete hooping on my fabric.  After stitching the design----it said "Biscornu" to me.  So I stitched a second one to make my Biscornu.  Biscornu defined is a French adjective that means "that which has an irregular form, with projections" or "complicated and bizarre".  It is a tiny eight-sided pillow, that depending on it's size can be a pincushion, holiday ornament, key chain/cell phone decoration or scissors fob, or fill with potpourri or herbs for a sachet.
 
To make one you need two square designs the exact same size. It is helpful to have a running stitch border stitched around it but I drew my border where my basting stitches had been.  Measuring very carefully mark and then match one corner point on one square to the center point on the side of the other square.  On the underside stitch these two points together.  (Having folded and pressed under the edges ahead of time is helpful.)
 
Now begin stitching the sides together, matching the next corner and center point along the way.  If you did NOT have a running stitch border to begin with, you can stitch them together  with fabric right sides together, leaving a side open for turning.  Turn, push out points and stuff.  Close your opening and stitch along the seam line with a decorative stitch using embroidery floss or you can bead it.  Add a button  to each side of the pillow pulling them together some what to complete your biscornu.
 
If you have a running stitch border, you would match the center point of each side with a corner point with wrong sides  of fabric together and joining together with the embroidery floss as you go. Complete with stuffing and buttons.
 
I'm using this one as a pincushion.  I love decorative and useful pinchusions.  I would love to see you design some designs for actual Biscorns patterns.  I would even like one done in an 8x8 size to make some toss pillows.  Digitize some in like a 2x2 fob size, the 5x5 for a pincushion and the 8x8 for a toss pillow, and I'll test and make them for you.