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研究生： 李珮欣
Pei-Hsin Lee
論文名稱： 正多面體的動態模擬
The Animation of Regular Polyhedrons
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： 96
語文別： 英文
論文頁數： 57
中文關鍵詞： 正多面體 、動態模擬
外文關鍵詞： Regular Polyhedron, Animation
相關次數： 點閱：3  下載：0 
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    • 在本篇論文中，透過3D動態幾何軟體Cabri 3D的動畫效果，呈現五種正多面體經由一些幾何性質的變化後，形成另一個多面體，例如正四面體可以變成Triakis Tetrahedron，正立方體可以變成Rhombic Dodecahedron，正八面體變成Stella Octangula，正十二面體變成Great Dodecahedron，正二十面體變成Great Icosahedron…等，在以下的網頁中可以清楚地看到正多面體的動態模擬與作圖過程：
    http://apollonius.math.nthu.edu.tw/d2/thesis-2008/Lee/
    透過這個網頁，每個人可以清楚的看到與操作多面體的變化與Cabri 3D軟體的應用發展。

    In this thesis, I would like to perform transformation of five kinds of regular polyhedron to other polyhedrons by their geometry properties. For instance, Triakis Tetrahedron can be transformed from Regular Tetrahedron; Rhombic Dodecahedron can be transformed from Cube; Stella Octangula can be transformed from Regular Octahedron and Great Icosahedron can be transformed from Regular Icosahedron, etc.

    The following website shows clearly the dynamic simulation and detail process of generating regular polyhedron.
    http://apollonius.math.nthu.edu.tw/d2/thesis-2008/Lee/

    The variety of polyhedron and the application and development of Cabri 3D are displayed on the website as well.

    Section 1 The Animation of Regular Tetrahedron Section 1-1 Tetrahedron Net ‥‥1 Section 1-2 Triakis Tetrahedron ‥‥3 Section 1-3 Truncated Tetrahedron‥‥4 Section 2 The Animation of Cube Section 2-1 Cube Net ‥‥5 Section 2-2 Rhombic Dodecahedron‥‥8 Section 2-3 Truncated Cube ‥‥10 Section 3 The Animation of Regular Octahedron Section 3-1 Octahedron Net ‥‥12 Section 3-2 Cuboctahedron ‥‥15 Section 3-3 Stella Octangula (PartI PartII)‥‥17 Section 4 The Animation of Regular Dodecahedron Section 4-1 Dodecahedron Net ‥‥21 Section 4-2 Small Stellated Dodecahedron ‥‥24 Section 4-3 Great Dodecahedron (PartI PartII)‥‥26 Section 4-4 Dodecadodecahedron (PartI PartII)‥‥30 Section 4-5 Icosidodecahedron ‥‥34 Section 4-6 Truncated Dodecahedron ‥‥36 Section 5 The Animation of Regular Icosahedron Section 5-1 Icosahedron Net ‥‥38 Section 5-2 Great Icosahedron (PartI PartII)‥‥41 Section 5-3 Icosidodecahedron ‥‥47 Appendix ‥‥49 Reference ‥‥57

    1. http://mathworld.wolfram.com/TriakisTetrahedron.html
    2. http://mathworld.wolfram.com/TruncatedTetrahedron.html
    3. http://mathworld.wolfram.com/RhombicDodecahedron.html
    4. http://mathworld.wolfram.com/TruncatedCube.html
    5. http://mathworld.wolfram.com/Cuboctahedron.html
    6. http://mathworld.wolfram.com/StellaOctangula.html
    7. http://mathworld.wolfram.com/SmallStellatedDodecahedron.html
    8. http://mathworld.wolfram.com/GreatDodecahedron.html
    9. http://mathworld.wolfram.com/Icosidodecahedron.html
    10. http://mathworld.wolfram.com/TruncatedDodecahedron.html
    11. http://mathworld.wolfram.com/GreatIcosahedron.html
    12. http://mathworld.wolfram.com/Dodecadodecahedron.html
    13. http://zh.wikipedia.org/w/index.php?title=%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94&variant=zh-tw
    14. http://zh.wikipedia.org/wiki/%E5%8D%8A%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94
    15. http://www.linksoft.com.tw/Products/Cabri3D.html (The improvement of Cabri 3D's versions)
    16. http://www.hcsh.tp.edu.tw/~math01/Cabri3D/index.html (The application of Cabri 3D in high school mathematics)

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