Anyway, yes, Natalie and Fiona were right: it is a stocking stitch Baktus, known as a Karius. The edges are meant to roll and some people put decorations on the points, such as beads. I am going to do that with this one. I am in that state where I want to knit everyone a Baktus or a Karius for Christmas, with ribs and stripes and all the possible variations, but I expect that will pass.
The clue was the set of scales I finally bought, because you have to keep checking the weight of the remaining yarn until you're half way through and then you start decreasing.
Reversible Knitting again

I mentioned Reversible Knitting recently: a helpful commenter on Jean's blog pointed out that if you go to Melanie Falick's blog and scroll down, you will find a link in the sidebar to the book.
When you click on it, it pops open a slide-show of some spreads from the book. Jaw-dropping.




