The process of working out how to make a pentagonal box (with lid) was productive in more ways than one.
Having had to work out all the folds from first principles, as opposed to copying them from the book (a hexagonal box is two pages of instructions and you have to change some of them to make a nesting base), I've found that I can now do many other boxes without needing to look at the book.
I now have a much better understanding of what fold is producing what part of the final box (trust me, when I say that this is not intuitively obvious) and am much more confident at tweaking the instructions to produce different styles of boxes. I've done three totally different triangular box styles now, in addition to the ones in the book.
Triangles are the most amenable to variation as you have more free paper to play with. Hexagons and pentagons have (as far as I can work out) a very limited number of permutations as the way in which you have to join the pieces together doesn't allow for many frills. This limitation may only apply to boxes that use less pieces of paper than they have sides (eg. the pentagon and hexagon both use two pieces of paper, wheras the triangle uses three), but I haven't yet tried looking into a hexagonal box that uses six pieces of paper. There is a chance that it will prove impossible using square paper, as there will come a point when there won't be enough paper left, after folding the rim, to reach into the centre.
It's proving to be an interesting blend of geometry, occasional trig and general logic. It's also one of the few things I can do at present that doesn't cause pain. (I hurt my neck last week and although it has improved, it still isn't normal - even watching TV is uncomfortable) The really annoying thing is that the pain is fuzzing my brain. I look at an origami problem and make way too many stupid mistakes. Last night, I managed to convince myself that half of 3/4 was 1/3 ! (And it was several minutes before I spotted the mistake)
I want to stop hurting and I want my brain back!
If you want to see what I've been making, entorien
will have some of them for sale in the Orbital dealer's room. The price will not reflect the time it takes to make them. It's not uncommon for a box to take a couple of hours to fold and assemble - the ones with flowers and birds on top are staggeringly complicated.