I think I've found the cause of my eczema: K.'s apartment.
Or rather the stairs leading up to it. They're very steep and when I go down them, my legs always brush against the step above.
This, I believe, may cause skin-to-carpet contact, as my trouser legs ride up from the friction with the floor covering. Most of the patches on my legs are just above my ankles, above the top of my socks, exactly where thy touch the stairs. Apparently I'm either allergic to something in the carpet or there is a fungus in it. (The latter goes to show it doesn't always pay to be such a good hostess. At least not to fungi...)