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Zwei bemerkenswerte bewegliche Strukturen

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Abstract

Two overconstrained mechanisms are presented that both are related to regular polyhedra in the Euclidean 3-space. The first example, the HEUREKA-polyhedron, is a modification of BUCKMINSTER-FULLERS Jitterbug [1]. The spherical joints at the vertices of 8 regular triangles are replaced by particular cardan joints. A 15m high model of this polyhedron was exhibited at the national research exposition of Switzerland 1991 in Zürich. Further the GRÜNBAUM-framework is discussed. Here the 10 regular tetrahedra inscribed to a regular pentagon-dodecahedron are linked together at the common vertices. This framework allows at least two types of constrained motions. The first was found by R. Connelly [2]. These motions preserve the fivefold symmetry with respect to any face axis. Motions of the two second type preserve the symmetry with respect to any vertex axis.

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Literature

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Authors and Affiliations

  1. Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/113, A 1040, Wien

    Hellmuth Stachel

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  1. Hellmuth Stachel
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Vortrag, gehalten aus Anlaß der Ehrenpromotion von Herrn Prof. Dr. W. Wunderlich an der TU München am 6. November 1991.

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Stachel, H. Zwei bemerkenswerte bewegliche Strukturen. J Geom 43, 14–21 (1992). https://doi.org/10.1007/BF01245938

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  • DOI: https://doi.org/10.1007/BF01245938

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