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Volume 16 Issue 1
Mar 2005
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Ying Chen, Jue Peng, Jingzhong Chen, Guangzhi Long. Stereographic Projections of Symmetry Elements and Single Forms on Quasicrystals. Journal of Earth Science, 2005, 16(1): 16-23.
Citation: Ying Chen, Jue Peng, Jingzhong Chen, Guangzhi Long. Stereographic Projections of Symmetry Elements and Single Forms on Quasicrystals. Journal of Earth Science, 2005, 16(1): 16-23.

Stereographic Projections of Symmetry Elements and Single Forms on Quasicrystals

Funds:

the National Natural Science Foundation of China 48970082

the National Natural Science Foundation of China 49272091

  • Received Date: 27 May 2004
  • Accepted Date: 20 Dec 2004
  • In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.

     

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  • Peng, Z. Z., 1985. Building Principles of Quasicrystal and the Particle Fractal Structural Model. Earth Science—Journal of China University of Geosciences, 10(4): 159-174 (in Chinese with English Abstract)
    Schechtman, D., Blech, I., Gratias, D., et al., 1984. Metallic Phase with Long-Range Orientational Order and no Translational Symmetry. Phys. Rev. Lett. , 53: 1951 doi: 10.1103/PhysRevLett.53.1951
    Shi, N. C., Min, L. Q., Shen, B. M., 1991. Composing of Crystal Cells and Deducing of Crystal Lattice on Quasicrystals. Science in China(Series B), (11): 1216-1223 (in Chinese with English Abstract)
    Zhao, W. X., Chen, J. Z., Wan, A. W., 1993. Point Groups and Single Forms of Quasicrystal. Earth Science—Journal of China University of Geosciences, 18 (Suppl. ): 25-41(in Chinese with English Abstract)
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