Patterned Polyhedra: Tiling the Platonic Solids
Patterned Polyhedra: Tiling the Platonic Solids
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图案多面体：平铺柏拉图立体
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
B. Hann
中科院分区：
文献类型：
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作者：
B. Hann
本文探讨了一系列几何概念的重要性，以进一步了解二维和三维设计。简要解释了图案和平铺的对称性，并将注意力集中在一组特殊的多面体上，即柏拉图立体。在试图将二维重复设计应用于正多面体时遇到的困难，避免间隙和重叠并确保精确的配准，是公认的。介绍了利兹大学正在进行的研究结果。确定了对该过程重要的对称特征，并解释和说明了五个固体中的每一个的图案。提出了进一步研究的途径。
This paper examines a range of geometric concepts of importance to the further understanding of twoand threedimensional design. A brief explanation is given of symmetry in patterns and tilings, and attention is focused on a particular set of polyhedra, known as the Platonic solids. The difficulties encountered in attempting to apply twodimensional repeating designs to regular polyhedra, avoiding gap and overlap and ensuring precise registration, are recognized. The results of ongoing research at the University of Leeds are presented. The symmetry characteristics of importance to the process are identified, and the patterning of each of the five solids is explained and illustrated. Avenues for further research are suggested.