Modular Origins - Tamatebako
In her posting this morning Dorothy Engleman give the URL for diagrams for the Temate Baku (it can be written in English as one word or two). At http://origami.kvi.nl/models/boxes/tematebk/temateb.1.gif
This brings up a single page, but the instructions for the Temate Baku are incomplete and there is no lead from that page to a second page. However, I replaced the "1" towards the end of the URL with a "2" and this brought up a second page which completed the model. Even so, the instructions do not seem to be complete. Step 12 show a triangle on each side of the puzzle purse being opened out, but it doesn't explain how the triangles are obtained. The triangle from each of two puzzle purses are stuck together and the cube built
up. the triangles are tucked in to give the finished figure. The instructions do not indicate that an "X" cuts are needed in the centre of each separate module.
On page 47, Kasahara gives a copy of the illustration from the three-volume woodcut book Ranma-Zushki (Ranma Sketches) by Hayato Ohaka, which was published in 1734. Among cranes, boats, sanbo and other folds, two examples of the cubic box are shown. Both have an "X" on each face and the way one is drawn suggests the appearance of a closed puzzle purse.
This print has been known in origami circles for some twenty years or more and was shown in Takagi's "Origami from the Classics" in 1993. It has been the subject of much discussion. The actual method of folding can really only be guessed at, but research by Masao Okamura, the Japanese historian of origami into later examples of modular cubes has suggested that the box in the print is made up of six puzzle purses. A puzzle purse is a kind of windmill fold made from a square of paper divided into nine smaller squares.
On page 49 of his book, Kasahara shows how to put together the six puzzle purses. First two cuts from corner to corner are made in the central square of each of the six squares of paper.. This enables four triangular flaps to be made. The six squares are the folded into puzzle purses in the usual way, leaving the triangular flaps sticking out at the back. The triangular flaps are then inserted into slots in the other puzzle purses and the cube is built up. Glue is not absolutely necessary, but it does help to maintain the stability
of the cube and I'm sure that in 1734, a folder would have considered it mad not to use glue. Anyway, I think it's one of the exceptions to the rule against glue that we discussed a week or so ago.
The Tamatebako so formed has a puzzle purse on each of its six faces, which can be opened and closed separately. Kasahara suggests that it may have been used as a kind of "tato" or container for bits and pieces.
So far as can be seen, this is the first modular folding (with or without cuts) that has been discovered, if indeed the present interpretation of the figure on the woodcut of 1734 is the correct one.