1. The peritectic reaction occurs in the icosahedral quasicrystal formation.

2. The renormalization group treatment and the icosahedral subgroup approximation to SU(2) are used.

3. In chapter 3, the elastic deformation in icosahedral clusters was calculatedanalytically and a numerical simulation was performed to test the theory.

4. It was indicated that structural protein of icosahedral viruses capsid in fact take on various conformations.

5. Octahedral and icosahedral tessellations work well and are notvery difficult to implement.

6. Satellite Tobacco Mosaic Virus is a small, icosahedral plant virus which worsens the symptoms of infection by Tobacco Mosaic Virus (TMV).

7. Results show that ability of forming Icosahedral symmetry of pure liquid metals is weaker than that of alloys.

8. It has linear double strand DNA, icosahedral - capsid and envelope.

9. The capsids of nearly all spherical viruses adopt icosahedral symmetry.

10. The microstructure, composition and phases of the alloy were analyzed by SEM and EDS. The icosahedral quasicrystal structure was identified by TEM.

11. It is found that, reverse to common idea, the short-range is notpreferable for the stability of icosahedral clusters.

12. The results of the pair analysis technique show that the icosahedral short-range order may grow with the decrease of the temperature and may become more prevalent in the undercooled state.

13. To investigate the proteins and structural features of HPV16 capsid will be valuable for understanding of viruses with icosahedral structure and potentially for vaccine design.

14. In this paper we explain the probability of existence on the body-center cubic and icosahedral phase and the transforming process.

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15. The principle and method of electron cryomicroscopy and computer three-dimensional reconstruction of icosahedral virus were described in detail, and some improvements were made in this thesis.

16. This paper deals with concerns the construction of an icosahedral quasilattice by the cut and project method.

17. By means of pair analysis technique and bond orientational order, we find that there exist a number of icosahedral short range units in the system.