Paula Nadelstern suggested, and I quote, "mirrors". Maybe she goes into more detail in the other book which I've just ordered. I know that she uses A4 to draft her kaleidoscopes, so the most she'd need would be 10" or 11" at any time. I can't recall her talking about a kaleidoscope bigger than 20" diameter.
Of course, I am probably a good couple of years away from being able to do kaleidoscopes like that, partly because I haven't yet learned how to use a sewing machine let alone to use it with deadly accuracy (my hand-piecing is excellent, but it seems that you need machine-piecing for this), partly because I don't think I have more than a couple of appropriate fabrics in my stash and will need to build that up (all the good ones seem to be sold overseas, drat it), and also I don't know if I'm up to the challenge artistically, though I'd certainly like to try. But I might experiment with something smaller scale in the meantime, and I'm interested in seeing if I can apply the technique to making quilts using complex Islamic geometric designs. Hmm, I wonder if Jinny Beyer mentions mirrors in her books at all? She's very into using border prints in a basic kaleidoscope way.