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Reference
Helena Verrill: Origami Tessellations. In: Bridges 1998. Pages 55–68
DOI
Abstract
Origami tessellations are made from a single piece of paper, which is folded in a repeating pattern. Figure l.a shows an example of a crease pattern for an origami tessellation. This pattern was created with the aim of producing a finished pattern of repeating "heart" shapes.
The problem of finding tessellations which can be folded is difficult because the paper must not be stretched or cut, and must end up as a flat sheet, so this imposes many conditions on the pattern to be folded. An understanding of the geometry of tessellations and of paper folding is required. However, the study of paper folding is still in its infancy, and many questions which have been an- swered for Euclidean constructions remain unanswered for origami methods; for instance, although impossible with Euclidean geometry, it is simple to trisect an angle using folding techniques, (see [HU2I]). However a satisfactory list of axioms, and a list of exactly what is possible, and what is not possible, for origami-geometry constructions has not been found conclusively, though several attempts have been made (See [H4)). On the other hand, though some geometric constructions may be easier with origami, the problem of determining whether a crease pattern can be collapsed to give a flat origami, or even folded at all, is generally very difficult (see [BH] and [K]). ...
Extended Abstract
Bibtex
Used References
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[V4] H. Verrill, Origami weave patterns and star patterns, preprint, May 1998.
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Full Text
http://archive.bridgesmathart.org/1998/bridges1998-55.pdf
