Michael Adams wrote:

However as soon as you fold it once in the other direction, after
having folded it twice already, you must have a fold in three sides.

Yes, that's right. There is a fold of three sides of the *paper*, but that
is not the same as saying that there is a fold on three edges of the *book*.
A book only has three edges (top, bottom and fore-edge). The fourth side is
the spine, where the signatures are sewn together.

What you seem to be saying here, is that a book can indeed have three
sides with folds. In this case bottom, fore edge, and spine. Which
is what I was suggesting for this book.

I can quite see that that was what you *meant*, but what you actually *said*
was:

Its impossible to fold a sheet of book paper so the folds
only occur on two edges of the finished book.

That is incorrect, because - as I say - a book only has three edges, only
two of which (in an octavo book) will normally have folds. So we are in
agreement that three out of four sides of the pages of an octavo book will
have folds. The confusion arises when you try to count the spine as an
"edge" of the book. It isn't.

Except I was suggesting the side without folds was
the fore edge, rather than the top.

That's a possible variant, but the more usual arrangement is for the bottom
edge to be the one without folds. But the weird and wonderful ways of
bookbinders sometimes defy logic. I have in front of me right now, for
example, a copy of Stevenson's Underwoods, in which the signatures consist
of eight leaves (i.e., octavo), but the distribution of opened and unopened
edges is very peculiar. The pages have all been opened, so all I have to go
on is uncut edges (where the logical assumption is that there *was* a fold
at some point) versus smooth edges (where there was no fold). Most of the
pages are uncut at the top edge and fore-edge, as one would expect, but
there are scattered leaves (not according to any pattern that I can observe)
which have *all three* edges uncut. Sometimes there is just one such leaf,
sometimes two or three together. I'm assuming that the third fold must have
been opened *before* the actual binding took place, since if it had been
bound with folds on all three edges there would have been nowhere to insert
the blade and it would have been impossible to open the pages, but I'm still
not sure what procedure led to this result. It's quite a small book, so at
first I hypothesised that each octavo signature was actually made up of
*half* an original sheet, but that wouldn't give the same distribution or
overall number of uncut edges.

--
John
http://rarebooksinjapan.com