I just finished making a pair of socks from Anna Zilboorg's great book, Socks for Sandals and Clogs. I love this book because of the clever patterning that she puts down the backs of the sock heels, which you can see in the picture below. Here, the heel is folded up over the sole so you can see it.
Most socks just have a rather generic heel flap, I suppose because when you wear regular shoes, the heel flap doesn't show. But a lot of people wear clogs and Birkenstock-type sandals nowadays, and some people wear socks with their clogs. I always wear socks with my Birki plastic clogs, because they're not very comfortable without socks. (Otherwise, the plastic pulls the little hairs on the tops of my feet and toes, which I suppose you are supposed to shave off if you're a good girl.)
I spun a wool/mohair/nylon blend for these socks, fairly tightly, and plied it balanced. It knitted up at a gauge of about six stitches per inch on 3mm needles.
There is a lace pattern that travels down the front and back of each sock:
This pattern was sort of a challenge for me. I had to learn how to do a raised increase. After I learned this, the pattern became easy. Ana Zilboorg also uses raised increases on the toe of her toe-up patterns, of which this is one.
I have ambivalent feelings about toe-up socks. On the one hand, if you're not sure you have enough yarn to make a tall sock, you can start at the toe and just knit until you run out of half your yarn. (Then make the other one.) On the other hand, I don't like the fiddly cast-on for toe-up socks. But the more times I do it, the easier it gets.
With this pair of toe-up socks, I didn't do the heel the way AZ suggests for the first sock. I knitted a tube from toe to the top of the sock; then I inserted a plain heel. For the second sock, I did it her way: I knitted up to where the heel would start, put the sock aside, made a new "toe," which would actually be the heel, and grafted it onto the sole stitches, and then joined the round and away I went up the ankle. This worked marvelously well, and I admire her innovation in the "unventing" (as Elizabeth Zimmerman used to say) of this technique. It's not traditional, but it works!
The picture below shows how the heel joins the ankle, and how it looks from the back of the sock.