| Part I --- Introduction and Preliminaries |
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Section I | Introduction |

Section II | A Special Note on the Notations |

| Part II --- Symmetric Solid Object Basics |
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Section III | Basic Properties of the Tetrathedron |

Section IV | Basic Properties of the Cube |

Section V | Basic Properties of the Octohedron |

Section VI | Basic Properties of the Dodecahedron |

Section VII | Basic Properties of the Icosahedron |

| Part III --- The Tetrahedron, tbe Cube , and the Octahedron |
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Section VIII | The Bi-Symmetric Nature of the Tetrahedron |

Section IX | The Bi-Symmetric Nature of the Cube |

Section X | The Tri-Symmetric Nature of the Cube |

Section XI | The Bi-Symmetric Nature of the Octahedron |

Section XII | The Quad-Symmetric Nature of the Octahedron |

Section XIII | Brief Summary on the Tetrahedron / Cube / Octahedron |

| Part IV --- The Dodecahedron |
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Section XIV | Bi-Polar Structures within the Dodecahedron |

Section XV | The Bi-Symmetric Nature of the Dodecahedron |

Section XVI | The Tri-Symmetric Nature of the Dodecahedron |

Section XVII | The Quad-Symmetric Nature of the Dodecahedron |

Section XVIII | The Hexa-Symmetric Nature of the Dodecahedron |

| Part V --- The Icosahedron |
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Section XIX | Bi-Polar Structures within the Icosahedron |

Section XX | The Bi-Symmetric Nature of the Icosahedron |

Section XXI | The Quad-Symmetric Nature of the Icosahedron |

Section XXII | The Penta-Symmetric Nature of the Icosahedron |

Section XXIII | The Deci-Symmetric Nature of the Icosahedron |

Section XXIV | The [ 2-6-6-6-Symmetry ] co-existing within the Icosahedron |

Section XXV | [ Quad-Type Structures ] within the Icosahedron |

| Part VI --- Bringing-in the Spherical Solid Objects |
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Section XXVI | Defining Great-Circles , Great-Cricle-Planes and Great-Circle-Arcs |

Section XXVII | The Tetrahedral Sphere ( 4-Split ) |

Section XXVIII | The Quasi-Cubic Sphere ( 6-Split ) |

Section XXIX | The Octahedral Sphere ( 8-Split ) |

Section XXX | The Dodecahedral Sphere ( 12-Split ) |

Section XXXI | The Icosahedral Sphere ( 20-Split ) |

Section XXXII | Ratio-Of-Areas and the Egyptian Fractions |

| Part VII --- Duality Considerations |
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Section XXXIII | Duality - Tetrahedron vs. Tetrahedron |

Section XXXIV | Duality Linkage via the [ TFS ( 24-Split) Sphere ] |

Section XXXV | Duality - Cube vs. Octahedron |

Section XXXVI | Duality Linkage via the [ FES ( 48-Split ) Sphere ] |

Section XXXVII | Duality - Dodecahedron vs. Icosahedron |

Section XXXVIII | Duality Linkage via the [ OHATS ( 120-Split ) Sphere ] |

| Part VIII --- Structure of the [ Quad-Type Structures ] within the Icosahedron |
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Section XXXIX | Identifying 2 [ Quad-Type Structures ] for Our Analysis |

Section XXXX | A First Look at the 2 [ Quad-Type Structures ] |

Section XXXXI | Rotational Orientation of the [ Curved Triangular Pieces ] |

| Part IX --- 5-Colors Combinatorics for the [ Quad-Type Structure Coloring Schemes ] |
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Section XXXXII | A Special Feature of the [ Quad-Type Coloring Schemes ] |

Section XXXXIII | 5-Colors Combinatorics for the [ ALPHA Series ] |

Section XXXXIV | 5-Colors Combinatorics for the [ OMEGA Series ] |

| Part X --- Concluding Remarks |
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Section XXXXV | Concluding Remarks |