1. Introduction. Recently I was looking for a simple but interesting model which a class of students could complete in about twenty minutes, which would illustrate groups of symmetries in three-dimensional space. My thoughts went back to the lampshade described in the Gazette for June 1971 (No. 393, pp. 310–312) but I felt that it would take too long to make, even if each student merely cut out a strip which I had marked out beforehand. Forced in this way to reconsider the matter, I found that the last sentence of my article was false—there are in fact four other such structures, which I now describe.