2011

Dynamic Geometry

  • Thesis

Edge Length and Volume of Seven-compounds

Small Rhombicosidodecahedron and Its Compound Small Rhombicosidodecahedron and Its Compound
  • Small Rhombicosidodecahedron Dodecahedron Icosahedron Cube
    Edge a 1 2 3 5 - 3 a 1 2 3 5 - 1 a 1 2 9 + 4 5 a
    Volume 2 0 + 2 9 3 5 a 3 1 4 1 3 5 + 2 7 5 a 3 5 1 2 3 9 + 3 7 5 a 3 3 8 + 1 7 5 a 3

  • Ratio

    • Edge ratio = 2 : 3 5 - 3 : 3 5 - 1 : 9 - 4 5
    • Volume ratio = 2 4 0 + 1 1 6 5 : 4 0 5 + 8 1 5 : 1 9 5 + 1 8 5 5 : 3 5 6 + 2 0 4 5
Compound of a Dodecahedron, an Icosahedron, and Five Cubes Great Rhombicosidodecahedron and Its Compound
  • Great
    Rhombicosidodecahedron    		 Dodecahedron Icosahedron Cube
    Edge a 5 2 5 - 1 a 3 2 1 + 5 a 3 + 2 5 a
    Volume 9 5 + 5 0 5 a 3 1 2 5 4 5 + 5 a 3 4 5 4 1 1 + 5 5 a 3 2 0 7 + 9 4 5 a 3

  • Ratio

    • Edge ratio = 2 : 5 5 - 5 : 3 + 3 5 : 6 + 4 5
    • Volume ratio = 3 8 0 + 2 0 0 5 : 6 2 5 + 1 2 5 5 : 4 9 5 + 2 2 5 5 : 8 2 8 + 3 7 6 5
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Advisor: Prof. Jen-Chung Chuan
Student: 邱柏榮