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Introduction; The Octahedral Group; The Octahedral Double Group; The McKay Correspondence; Lie Groups and Lie Algebras; Coxeter’s Reflection Groups; Thom–Arnold Catastrophe Structures; ALE Spaces and Gravitational Instantons; Knots and Links and Braids; Twistors and ALE Spaces; 2-Dimensional Conformal Field Theories; Elliptic Curves and the Monster Group; Sphere Packing and Error-Correction Codes; Qubits and Black Holes; The Holographic Principle; Calabi–Yau Spaces; Heisenberg Algebras; Summary and Outlook; Glossary; References and Bibliography

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