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Pentagonal origami boxes
As a few of you will know, I've been happily folding origami boxes of various shapes and sizes since Xmas. They're complex enough to provide a good focus for relaxation and not so difficult that I can't do them when I'm stressed. (the shoulder is so bad at the moment that cross stitch, my normal relaxation, is proving painful)
Gradually, I've been finding errata in the book I'm using. Not too many of them, but enough to make me think about the mathematics behind the way they are folded and why particular folds are necessary to make a box of a particular shape.
The book gives instructions for square, hexagonal and octagonal boxes. I've been thinking for a while about how to do a pentagonal box and finally succeeded in folding one this morning. The process reveals several things about the design of some of the other boxes, such as the choice for the depth of the rim.
I had to cheat in one small respect. Purist origami uses no rulers or protractors. Playing around with the geometry, I realised that I'd have to measure an angle of 18 degrees to do the first fold (this eventually gets me to the necessary angle of 54 degrees between the base of a side and a line into the centre of the pentagon).
Playing around with trigonometry, I think I may have found a way of getting an angle of (almost) 18 degrees without having to use a protractor. It relies on folding a piece of paper in three. This isn't that easy to do, but a bit of trial and error will get you there pretty quickly. Maybe later today, I'll try doing a box that way and see if it works. (If it's more than a degree out, I'll probably end up with a hole in the centre of the box lid, or else a small dome).
After that, the hard part will be writing down the instructions in a clear manner. There's some folds that aren't needed other boxes and I need to be able to describe precisely where they are. I may need to co-opt Richard to draw the diagrams for me as I demonstrate step by step.
I'm sure someone must have done pentagonal boxes before, but I don't see any books that contain instructions on Amazon (one book has a septagonal box - more correctly 'heptagonal').
Has anyone else come across a pentagonal box?
Gradually, I've been finding errata in the book I'm using. Not too many of them, but enough to make me think about the mathematics behind the way they are folded and why particular folds are necessary to make a box of a particular shape.
The book gives instructions for square, hexagonal and octagonal boxes. I've been thinking for a while about how to do a pentagonal box and finally succeeded in folding one this morning. The process reveals several things about the design of some of the other boxes, such as the choice for the depth of the rim.
I had to cheat in one small respect. Purist origami uses no rulers or protractors. Playing around with the geometry, I realised that I'd have to measure an angle of 18 degrees to do the first fold (this eventually gets me to the necessary angle of 54 degrees between the base of a side and a line into the centre of the pentagon).
Playing around with trigonometry, I think I may have found a way of getting an angle of (almost) 18 degrees without having to use a protractor. It relies on folding a piece of paper in three. This isn't that easy to do, but a bit of trial and error will get you there pretty quickly. Maybe later today, I'll try doing a box that way and see if it works. (If it's more than a degree out, I'll probably end up with a hole in the centre of the box lid, or else a small dome).
After that, the hard part will be writing down the instructions in a clear manner. There's some folds that aren't needed other boxes and I need to be able to describe precisely where they are. I may need to co-opt Richard to draw the diagrams for me as I demonstrate step by step.
I'm sure someone must have done pentagonal boxes before, but I don't see any books that contain instructions on Amazon (one book has a septagonal box - more correctly 'heptagonal').
Has anyone else come across a pentagonal box?