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Mathematical crystallography was developed to provide a unifying method for understanding crystal symmetry based on matrix algebra. The external symmetry of mineral crystals is often controlled by the internal symmetry of the atomic arrangement. The mathematics behind this internal symmetry is examined and explained in great detail.
Topics covered in Chapter 13 include:
Matrix Representation of Symmetry Operations Rotoinversion Axes Derivation of Space Group Symmetry Operations The Metric Tensor Volume Calculations Bond Distances BondAngles d-spacings and Reciprocal Space Angles Between Two Axes Angles Between Two Planes Angles Between an Axis and a Plane Normal Derivation of the 32 Crystallographic 3-D Point Groups Proper Point Groups Improper Point Groups Grouping the 32 Point Groups into the Six Crystal Systems A Brief Introduction to Linear Algebra and Matrix Manipulation as Applied to Mineralogy Multiplication of Matrices Transpose of a Matrix Inversion ("Division") of Matrices The Determinate of a Matrix Addition and Subtraction of Matrices Dot Products Cross Products The General Cartesian Rotation Matrix and Its Use in Mineralogy