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研究生： 王慧盈
Wang, Hui-Ying
論文名稱： Connectivities Among the Wire-Frame Models of Regular Polyhedrons
指導教授： 全任重
Chuan, Jen-Chung
口試委員: 李明恭
李華倫
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： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 43
中文關鍵詞： 柏拉圖多面體
外文關鍵詞： Wire-Frame Models, Regular Polyhedrons
相關次數： 點閱：2  下載：0 
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    • In order to understand the relationships of the Platonic Solids, we observe the elementary properties and rotational symmetry of the Platonic Solids. A polyhedral compound is a polyhedron that is itself composed of several other polyhedrons sharing a common center. There are intersection points of polyhedral compound.
    Finally, we get the Interesting combination of the five Platonic Solids.

    In order to understand the relationships of the Platonic Solids, we observe the elementary properties and rotational symmetry of the Platonic Solids. A polyhedral compound is a polyhedron that is itself composed of several other polyhedrons sharing a common center. There are intersection points of polyhedral compound.
    Finally, we get the Interesting combination of the five Platonic Solids.

    Abstract p2 Chapter 1. Introduction p4~5 1.1 Platonic Solids p4 1.2 Symmetry Axes of Platonic Solids p5 Chapter 2. Compound of Platonic Solids p11~20 2.1 Polyhedral Compound p11 2.2 Tetrahedron 2-Compound p11 2.3 Cube 2-Compound p12 2.4 Octahedron 2-Compound p13 2.5 Dodecahedron 2-Compound p15 2.6 Icosahedron 2-Compound p17 2.7 Tetrahedron 5-Compound in a Dodecahedron p18 2.8 Cube 5-Compound in a Dodecahedron p19 2.9 Octahedron 5-Compound in a Dodecahedron p20 Chapter 3. The Relationships of Platonic Solids p21~39 3.1 The Smallest Tetrahedron Containing the Icosahedron p21 3.2 The Smallest Octahedron Containing the Icosahedron p23 3.3 The Smallest Cube Containing the Icosahedron p24 3.4 The Smallest Cube Containing the Dodecahedron p26 3.5 The Smallest Cube Containing the Octahedron p28 3.6 The Smallest Cube Containing the Tetrahedron p31 3.7 The Largest Cube Contained in the Dodecahedron p33 3.8 The Largest Tetrahedron Contained in the Dodecahedron p34 3.9 The Largest Octahedron Contained in the Icosahedron p36 3.10 An Interesting Combination of the Five Platonic Solids p40 Chapter 4. Reference p43

    [1]http://mathworld.wolfram.com/PolyhedronCompound.html
    [2]http://mathworld.wolfram.com/Tetrahedron 2-Compound.html
    [3]http://mathworld.wolfram.com/Cube2-Compound.html
    [4]http://mathworld.wolfram.com/Octahedron 2-Compound.html
    [5]http://mathworld.wolfram.com/Dodecahedron 2-Compound.html
    [6]http://mathworld.wolfram.com/Icosahedron 2-Compound.html

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