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研究生： 許璧薇
Hsu, Pi-Wei
論文名稱： 多面體間的關係
Relations Between Polyhedra
指導教授： 張企
Chang, Chih
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： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 28
中文關鍵詞： Inscribed in a given polyhedron 、Escribed outside a given polyhedron 、Projection 、Intersection 、Inside-out
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    • There discuss that relations between polyhedron.
    In Chapter 2, we discuss (1) how polyhedron A having some extremal property be inscribed a given polyhedron B, where A and B can be any of the following types of polyhedron: the cube, regular tetrahedron, regular octahedron, regular dodecahedron and regular icosahedron. Then, we discuss (2) how the polyhedron can be regarded as a convex hull of other polyhedrons. Case (1) deals with two comparable polyhedrons and case (2) deals with two incomparable polyhedrons.
    In Chapter 3, we discuss how polyhedron A having some extremal property be exscribed outside a given polyhedron B, where A and B can be any of the following types of polyhedron: the cube, regular tetrahedron, regular octahedron, regular dodecahedron and regular icosahedron. Then, we discuss how the polyhedron can be regarded as a convex hull of other polyhedrons.
    In Chapter 4, we stress the projection of a rotating cube upon a given polyhedron. Because projecting a cube is easier than projecting.
    In Chapter 5, we discuss the intersection of polyhedrons. Here we address the question: How can a polyhedron be expressed as an intersection of several other regular polyhedrons?
    In Chapter 6, we constructed 12 animations showing how can a polyhedron be decomposed into disjoint pieces and then be “reassembled” into another polyhedron (with or without an empty spaces enclosed)?

    This thesis is to be accompanied with webpage http://m98.nthu.edu.tw/~s9821603/

    ABSTRACT Chapter 1 Introduction Chapter 2 Maximum Polyhedron Inscribed in a Given Polyhedron 2.1 Maximum regular tetrahedron included in a given cube 2.2 Maximum regular octahedron included in a given cube 2.3 Maximum cube included in a given tetrahedron 2.4 Maximum cube included in a given regular dodecahedron Chapter 3 Minimum Polyhedron Escribed Outside a Given Polyhedron 3.1 Minimum regular dodecahedron enclosing a given cube 3.2 Minimum cube enclosing a given regular octahedron 3.3 Minimum cube enclosing a given regular dodecahedron 3.4 Minimum regular tetrahedron enclosing a given regular icosahedron 3.5 Minimum cube enclosing a given regular Icosahedron 3.6 Minimum cube enclosing a given rhombic dodecahedron 3.7 Comprehensive: Minimum regular octahedron cube enclosed in a given regular dodecahedron ; Minimum regular tetrahedron enclosed in a given regular octahedron; Minimum cube enclosed in a given regular tetrahedron; Minimum regular Icosahedron enclosed in a given cube Chapter 4 Projection of Polyhedron upon a Concentric Polyhedron 4.1 Projection of a rotating cube upon a given fixed concentric cube 4.2 Projection of a rotating cube upon a given fixed concentric regular octahedron 4.3 Projection of a rotating cube upon a given fixed concentric regular dodecahedron 4.4 Projection of a rotating cube upon a given fixed concentric regular icosahedron 4.5 Projection of a rotating cube upon a given fixed concentric rhombic dodecahedron 4.6 Projection of a rotating cube upon a given fixed concentric diamond thirty icosahedron Chapter 5 Expressing a Given Polyhedron as Intersection of Well-Known Polyhedra 5.1 Bucky Ball can be expressed as an intersection of regular dodecahedron and regular icosahedron 5.2 Thirty sided rhombic can be expressed as an intersection of five cubes 5.3 Regular icosahedron can be expressed as an intersection of five regular tetrahedron 5.4 Regular icosahedron can be expressed as an intersection of five regular octahedron 5.5 Deltoidal icositetrahedron can be expressed as an intersection of four parallelepiped Chapter 6 Transforming the Faces of One Polyhedron Inside-Out 6.1 Transforming the faces of a cube inside-out 6.2 Transforming a cube into 24-faced polyhedron 6.3 Transforming a cube into 24-faced polyhedron with each face a triangle 6.4 Transforming the faces of a regular dodecahedron inside-out 6.5 Transforming a dodecahedron into 60-faced polyhedron 6.6 Transforming a dodecahedron into 60-faced polyhedron with each face a regular triangle 6.7 Transforming the faces of a regular icosahedron inside-out 6.8 Transforming a icosahedron into 60-faced polyhedron 6.9 Transforming the faces of a concave 60-Faced icosahedron inside-out each face a regular triangle 6.10 Transforming the faces of a cuboctahedron inside- out 6.11 Animation of 8 dipyramids and 6 octahedrons based on net expansion of cuboctahedron 6.12 Folding and unfoliding polyhedral nets

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