Regular Solids and Isolated Singularities [Paperback]

I: Regular Solids and Finite Rotation Groups.- ?1. The Platonic Solids.- ?2. Convex Polytopes.- ?3. Regular Solids.- ?4. Enumeration and Realization of Regular Solids.- ?5. The Rotation Groups of the Platonic Solids.- ?6. Finite Subgroups of the Rotation Group SO(3).- ?7. Normal Subgroups.- ?8. Generators and Relations for the Finite Subgroups of SO(3).- II: Finite Subgroups of SL(2,G) and Invariant Polynomials.- ?1. Finite Subgroups of SL(2,C).- ?2. Quaternions and Rotations.- ?3. Four-Dimensional Regular Solids.- ?4. The Orbit Spaces S3/G of the Finite Subgroups G of SU(2).- ?5. Generators and Relations for the Finite Subgroups of SL(2,C).- ?6. Invariant Divisors and Semi-Invariant Forms.- ?7. The Characters of the Invariant Divisors.- ?8. Generators and Relations for the Algebra of Invariant Polynomials.- ?9. The Affine Orbit Variety.- III: Local Theory of Several Complex Variables.- ?1. Germs of Holomorphic Functions.- ?2. Germs of Analytic Sets.- ?3. Germs of Holomorphic Maps.- ?4. The Embedding Dimension.- ?5. The Preparation Theorem.- ?6. Finite Maps.- ?7. Finite and Strict Maps.- ?8. The Nullstellensatz.- ?9. The Dimension.- ?10. Annihilators.- ?11. Regular Sequences.- ?12. Complete Intersections.- ?13. Complex Spaces.- IV: Quotient Singularities and Their Resolutions.- ?1. Germs of Invariant Holomorphic Functions.- ?2. Complex Orbit Spaces.- ?3. Quotient Singularities.- ?4. Modifications. Line Bundles.- ?5. Cyclic Quotient Singularities.- ?6. The Resolution of Cyclic Quotient Singularities.- ?7. The Cotangent Action.- ?8. Line Bundles with Singularities.- ?9. The Resolution of Non-Cyclic Quotient Singularities.- ?10. Plumbed Surfaces.- ?11. Intersection Numbers.- ?12. The Homology of Plumbed Surfaces.- ?13. The Fundamental Group of a Plumbed Surface Minus its Core.- ?14. Groups Determined by a Weighted Tree.- ?15. Topological Invariants.- V: The Hierarchy of Simple Singularities.- ?1. Basic Concepts.- ?2. The Milnor Number.- ?3. Transformation Groups.- ?4. l3‚