This is not faced. Facing has a large strip of fabric added and folded to the back. Like this:
https://thesillyboodilly.blogspot.co...y-to-face.html
This little mug rug has a "knife edge" finish. This can be achieved a few different ways. One way is to birth it before quilting as tesspug wrote. Then the piece was top stitched. I did the same thing on this little hexie table topper.
Hexagons
This method is best for small pieces like mug rugs, placemants, table toppers, etc. Anything bigger it gets dicey in the quilting process and you are likely to get pleats and tucks in the quilting.
The other way this can be done is a traditional knife edge where you turn under the backing and top 1/4" and top stitch or hand stitch closed, this was top stitched. There are loads of tutes out there and here is a link to Dread Pirate Rodgers pdf file that explains a lot of different ways to finish a quilt.
http://piraterodgers.com/tutorials/a...nishes/AF1.pdf