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Periodica Mathematica Hungarica

, Volume 39, Issue 1–3, pp 225–240 | Cite as

HIGHER ORDER FLEXIBILITY OF OCTAHEDRA

  • Hellmuth Stachel
Article
  • 40 Downloads

Abstract

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.

Keywords

Geometric Characterization Configuration Problem Order Flexibility Flexible Octahedra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Kluwer Academic Publishers 2000

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  • Hellmuth Stachel

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