Fig. 5. Fundamental region (module) of the polyhedral surface. latter surface is not a curved surface, and instead it is a polyhedral surface composed of the repetition of congruent parallelograms. Figure 3 shows it by a model. In 1978, Tanizawa and Miura (6) presented a proof by numerical computation that the hypothetical surface is really obtained by the biaxial contraction of an infinite plate. Figure 4 shows, by contour lines of the solutions, the transition from the postbuckling solution to the large displacement solution. The periodicity in two orthogonal directions is the most notable characteristic of this surface. In other words, the whole surface is constructed by the parallel transformation of a fundamental region, as shown in Figure 5, in the x and y directions. If this geometry is applied to the construction of a large membrane structure, the whole structure is constructed by the repetition of the identical module. Thus the difficulty in bunching a large blanket can be solved by this design. 2. PROPOSAL OF 2-D ARRAY CONCEPT The idea of the application of this surface to the packaging of planar large space structures was obtained immediately after these studies, but the time was not ripe. In 1978, in order to demonstrate the validity of the solution, Miura (3) applied its intrinsic geometry to map folding. The paper read at the 10th Conference of International Cartographers Association drew much interest from the attendants and thus was reported by articles in New Scientist (5) and British Origami (7) as the Miura-ori map; where “ori” comes from the origami — the paper folding art. Although map folding is simply a fine fun, it provides much useful information, which pure mathematics cannot do. For instance, we have learned from a Miura-ori map that the most important point of difference from an orthogonally folded map is that the folds are interdependent. Thus a movement along one fold line produces movement along the other. In other words, the map is automatically opened by just one pull at a corner. It means that, by the use of such mechanisms for the folding of a large blanket, it can be deployed automatically as well as biaxially. In 1980, Miura presented a paper entitled “Method of Packaging and Deploying of Large Membrane in Space” at the 31st IAF Congress, Tokyo (1). This was the first
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