期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 459, 期 2039, 页码 2847-2859出版社
ROYAL SOC
DOI: 10.1098/rspa.2003.1160
关键词
spherical circle packing; constrained Tammes problem; rigidity of packing; symmetry; optimization; compound of tetrahedra
How must 4N non-overlapping equal circles forming N quartets be packed on a sphere so that the angular diameter of the circles will be as large as possible under the constraint that, within each quartet, the circle centres lie at the vertices of a regular tetrahedron? Computer-generated solutions to this optimization problem are presented for N = 1-8 quartets. A check of Danzerian rigidity of the computed packings is made in each case. The configurations so obtained are characterized as compounds of regular tetrahedra, some well known and some newly defined.
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