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Rhombic Structures: Use of Mathematica in Combination with Solid Models for Studying Space Structures

Sándor Kabai
URL: http://www.kabai.hu

2006 Wolfram Technology Conference
Conference location

Champaign IL

Mathematica graphics are used to study space structures assembled from modular components. Relationships are explored among various subjects, such as fractals, Penrose tiling, quasicrystals, polar zonohedra, fullerenes, polyhedral clusters. A method is detailed for shaping polar zonohedra, which can be used to produce a variety of shapes, including torus, bullet, corn, heart, submarine, and domes, which can be used in architecture, for exploring spatial structures, and used for ornamental purposes. A cluster of 60 identical polyhedral units is introduced, as an alternative to the shape of truncated icosahedron. Rhombohedra and their parts are used to produce rings, helices, planar lattices, and space frames in which cubic and icosahedral symmetries are combined. Polyhedral clusters are shown as illustrations of various phenomena, such as phase change and crystal growth in metals and space filling. Polystyrene blocks, cut by the author with a hot-wire method, are shown to emphasize the benefits of the combined use of graphics, calculations done with Mathematica, and solid models for exploration of space structures. The suggested presentation is available for download from www.kabai.hu/RS.

*Mathematics > Geometry > Solid Geometry

RS1.ppt (13.5 MB) - Microsoft Powerpoint document
RS2.ppt (10.2 MB) - Microsoft Powerpoint document