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The problems in the accompanying exercises, "From 2D to 3D: Escher drawings", deal with abstractions that can be related to minerals through geometrical features they have in common. However, we are utimately interested in real minerals, their symmetries, and complexities. High-resolution transmission electron microscopy (HRTEM) provides 2-D projections of mineral structures at almost the atomic scale, and atomic force microscopy (AFM) provides 3-D information about the surfaces of minerals. By using these instruments, we can learn about defects in minerals and their complexities. The mineral examples in this problem set include representatives from several silicate structure type, sulfides, a sulfosalt, and a carbonate. Interpretation of the images is less clear-cut than of the idealized drawings. In some cases the results can be ambiguous, but the provide a scope for fruitful discussions among class members. In a few cases, references are given to the published papers from which the images are taken. These can be used to draw students into the professional literature, even though it will not always be possible to arrive at unambiguous answers. These problems should be thought provoking and yet manageable at several levels of complexity.
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