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研究生: 葉晉嘉
Chin-Chia Yeh
論文名稱: 與正十二面體相關的幾何構造
Geometric constructions associated with the regular dodecahedron
指導教授: 全任重
Jen-Chung Chuan
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2008
畢業學年度: 95
語文別: 英文
論文頁數: 32
中文關鍵詞: 正十二面體幾何
相關次數: 點閱:19下載:0
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  • 正十二面體是柏拉圖多面體其中的一個,由於正十二面體每一個面都是正五邊形。因此,提供了相當多的發展性,此篇論文藉由動態幾何軟體Cabri3D探討了正十二面體的相關性質,以及利用正十二面體出發建構了與星狀多面體或Catalan多面體相關之多面體。


    The regular dodecahedron has 12 faces and 20 vertexes. Each faces of the regular dodecahedron is a regular pentagon. In short, the regular dodecahedron can be employed in many ways. There are several sections in this study. For the first section, it talked about the duality of regular dodecahedron. The second and third section described about the relationship between regular dodecahedron and other stuffs. The fourth section discussed about using the regular dodecahedron to construct the certain polyhedrons. And, those polyhedrons are related to stellated polyhedrons. The final section talked about using the regular dodecahedron to construct the certain polyhedrons. And, those polyhedrons are related to Catalan solids.
    This paper presents the design of Polyhedron under Cabri3D, interactive dynamic software of geometry. It is divided into five sections. You can crystal clearly to discover the detail in the website:
    http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/g943251/dynamic/index.htm
    Here you can see the production of this study and application of 3D dynamic geometry.

    Contents 1.Abstract I 2.Preface II 3.Contents III 4.Preliminaries 1 5. Section 1: Duality of regular dodecahedron 2 6. Section 2: Geometric objects associated with the regular dodecahedron 4 7. Section 3: Constructions associated with a regular dodecahedron 7 8. Section 4: Constructions of polyhedrons associated with stellated polyhedrons by regular dodecahedron 12 9. Section 5: Constructions of polyhedrons associated with Catalan solids by regular dodecahedron 19 10.Appendix 27 References 32

    References
    [1] http://poncelet.math.nthu.edu.tw/
    [2] http://whistleralley.com/polyhedra/dodecahedron.htm
    [3] http://en.wikipedia.org/wiki/Dodecahedron
    [4] http://mathworld.wolfram.com/
    [5] http://cage.ugent.be/~hs/polyhedra/dodeicos.html
    [6] http://cage.rug.ac.be/~hs/polyhedra/dodeca.html
    [7] http://www.ac-noumea.nc/maths/amc/polyhedr/convex1_.htm
    [8] http://www.kjmaclean.com/Geometry/dodecahedron.html

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