I do not happily knit intarsia. I do not willingly strand while purling. But I really liked this heel pattern and there was no other way to do it. The intarsia is necessary only for a few rounds, and one can, on the heel, knit it backwards if purled stranding is an anathema.

The rest of the sock is plain knitting, which might make this the simplest sock, simpler than even Castor & Pollux, since all the complication is in one small area.