Contents
Chapter 1. Introduction 1
Chapter 2. Definitions of Polyhedra, Their Faces and Cones 5
2.1. Polyhedron 5
2.2. Faces of Polyhedron 7
2.3. A Cone (Dual Face) of Face 8
2.4. Generalized Newton Polyhedron 9
2.5. Basic Decompositions According to Faces and Cones 10
Chapter 3. Main Theorem and Background 13
3.1. Even Sets 13
3.2. Statement of Main Results 14
3.3. Background 17
Chapter 4. Combinatorial Lemmas 23
4.1. Elementary properties of faces and dual faces 23
4.2. Low Dimensional Polyhedron in Rn 24
4.3. Properties of Boundary and Interior of Face 26
4.4. Representations of Faces 27
4.5. Representations of Cones (Dual Faces) 29
4.6. Cone Decompositions 34
4.7. Projective Cone; Boundary Deleted Neighborhood 36
4.8. Representations of Unbounded Faces 40
4.9. Essential Faces 41
4.10. Invariance Property under Isomorphism 43
Chapter 5. Descending Faces vs. Ascending Cones 45
5.1. Construction of Descending Faces and Ascending Cones 46
5.2. Size Control Number 51
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