This first recipe will feature garter stitch, wrap 'n turn to hide the holes, and the standard opposing trapezoid construction.
I should mention that the garter stitch results in a softer, thicker fabric, because garter stitch is reversible. So it should wear harder, right? If you want, you can add reinforcement thread to make it super-tough. Also, because the garter stitch is thicker, it has a smaller row-gauge (takes more rows to go the same distance), so the resulting heel/toe is shallower and more rounded. It is also stretchier than a stockinette heel, so I find it fits me much better! But do a test first to see if it fits with your design. Finally, because of the garter bumps, the wraps remain hidden, and there is no need to lift them out of the fabric to knit them in when working up the second trapezoid. This is the only time that I, personally, use wrap 'n turns (because I have a hard time seeing the wraps on dark, fine wool).
Here we go. The pix show a practise heel that's smaller than you're likely to make, out of thicker wool so it's clearer for photos. And it's only over the heel sts, not the whole sock!
1. Get your heel sts on a single needle. Divide into thirds (roughly), making sure that the two edge portions have the same number of sts. If you have a wide heel, put more sts in the middle. Place 2 markers, one on each side of the middle third (those split-ring markers come in handy because you can just slide 'em in!).
[divide heel sts into thirds and place markers]
[stop before last st. Bring yarn forward...]
[slip last st to RH needle...]
[bring yarn to back...]
[slip that st back to the LH needle...]
[turn your work and put the yarn to the back ready for kntting again. That last st is "wrapped" with a loop around its feet. You don't knit it. Ready to start knitting the next row.]
Tip: Don't choke up on the wrap. It shouldn't be tight, it shouldn't scrunch the wrapped stitch over to its neighbour. If you tighten it too much, it causes "holes" in the fabric.
4. K until 1 st remains before last wrapped st, slipping the markers when you get to them. Wrap and turn.
5. repeat step 4 until you've wrapped all the sts on either side, and only the middle portion of the heel, between your markers, remains unwrapped. Knit across the middle sts, slipping the marker, and stop when you reach the first wrapped st (which should be the first st after the marker).
[here are a bunch of wrapped sts - kind of hard to see, but they all have their feet tied. Click to enlarge.]You've completed the first trapezoid and now it's time to start increasing the row lengths as you climb up the second, upside-down, trapezoid.
6. Slip the marker and wrap and turn the first st. It will now be double-wrapped.
7. Knit across the middle third, slipping the markers, to the first single-wrapped st on the opposite side. Just knit any double-wrapped sts you encounter (on the first time across, you won't encounter any, but after that, you will!). Wrap this single-wrapped st and turn. It is now also double-wrapped.
8. Repeat step 7 until you've double-wrapped (and then knit, on the next pass) every stitch on both sides of the heel.
[here is the practise heel. Click to enlarge. There are no holes.]
You are done with turning the heel. Easy, eh? No picking up those wraps required! It's all invisible thanks to the bumpy garter sts!
Knit across the instep - you may need to pick up a stitch in the "corner" between the heel and the instep, which you can k2tog on the subsequent round, to seal any holes.
This construction can also be used as a toe, in either top-down or toe-up constructions (both for a later post). Notice how round it is?
[same practise heel, folded the other way, for use as a toe!]
This is what it looks like in action (Cookie A design, Malabrigo sock yarn in Abril, worn lots!):
[wrap 'n' turn short-row garter heels]