>>> Will it be correct to say that there is a whole category 3D polyhedral surfaces, and it can appreciate different unique methods: Tachi's method, Chit's method and others. If it is so, what name would you give this > whole category? I really liked those criterions, with them Matthew described the Tachi's method. Is it possible to define the criteria for the whole category?
I would categorise Tachi's method as a way of folding a closed polyhedral surface. As I've mentioned, there are other ways. Adopting a strictly geometrical approach, there are basically the following forms: 1. 2D or flat folding - The model is first folded flat and takes the form of a silhouette. Folds may be later added to make it 3D. 2. Straight crease 3D - The model can be closed polyhedral or open polyhedral. The Gauss dome or saddle surface are non-developable, but a closed polyhedral surface with increasing number of facets is close to it. An open surface is where the folds or creases define the model. 3. Curved cease 3D - Either on their own or together with straight creases, they are used to create curved surfaces to simulate the Gauss curved surfaces. Also, there are closed and open forms. Where do tessellation, corrugation, pleating. paper crushing, and even flat folding techniques come in? They are used to create the model form or add features to it. For example, Lang's carp in Origami Design Secrets is flat folded. Tessellation provides the feature of the carp's scales. By varying the size of the individual scales, you can give the carp a 3D rounded shape. See also my arowana at: http://www.flickr.com/photos/chengchit/920490412/in/photostream The above are my personal opinions and are presented purely for discussion. Cheng Chit
