HIGHER ORDER FLEXIBILITY OF OCTAHEDRA
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More than hundred years ago R. Bricard determined all continuously flexible octahedra. On the other hand, also the geometric characterization of first-order flexible octahedra has been well known for a long time. The objective of this paper is to analyze the cases between, i.e., octahedra which are infinitesimally flexible of order n > 1 but not continuously flexible. We prove explicit necessary and sufficient conditions for the orders two, three and even for all n < 8, provided the octahedron under consideration is not totally flat. Any order ≥ 8 implies already continuous flexibility, as the configuration problem for octahedra is of degree eight.
KeywordsGeometric Characterization Configuration Problem Order Flexibility Flexible Octahedra
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