, Volume 39, Issue 1-3, pp 213-223

MECHANISMS OF THE ICOSAHEDRAL COMPOUND OF TEN TETRAHEDRA

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Abstract

Ten regular tetrahedra can be arranged in such a way that their vertices are coincident with the vertices of a regular dodecahedron and that two tetrahedra meet at each vertex of the dodecahedron. If the resultant structure is considered as a bar-and-joint structure, there will be 60 bars, lying along the edges of the tetrahedra, and 20 joints at the vertices of the dodecahedra; six bars meet at each joint. Although the structure more than satisfies Maxwell's rule, it is known to admit finite mechanisms.

Recently, a new method for detecting symmetric finite mechanisms in symmetric bar-and-node structures has been developed. The method only requires a count of the number of bars, and the number of nodes, that are left unmoved by each of the symmetry operations allowable for the structure. This paper will describe the application of this method to the structure described above. The structure has icosahedral symmetry, I h , and the analysis confirms the existence of the mechanisms with C 3v and C 5v symmetry that have previously been detected using ad-hoc methods.

This revised version was published online in August 2006 with corrections to the Cover Date.