engleski

Teaching point groups using modular origami

Symmetry is an essential concept for chemistry and during their education future chemists learn about molecular and crystal symmetry. This is usually limited to basic geometrical aspects of symmetry and “mechanical” usage of tables (e.g. character tables, diagrams for determination of point groups). Consequently, the knowledge about symmetry mostly remains on the intuitive, mathematically superficial, level, with little or no understanding what terms like “character”, “point group”, etc., really mean. Although this is often sufficient, a deeper mathematical knowledge of the matter can support thorough understanding of chemical topics. The drawback is that teaching group theory and other abstract notions requires a significant amount of time, and the usual teaching materials are written in a technical style that is hard to read and understand. Polyhedra models have been used for a long time in teaching symmetry and point groups. Such cardboard models have the disadvantage that they are easily destroyed, and their construction can be untidy and time-consuming. Modular origami is a technique of making paper models from several units folded from rectangular paper sheets and assembled into the final model, without gluing, so the model is easily dis- and reassembled. These models are usually developed from an aesthetic viewpoint, and mostly have cubic and icosahedral point groups. This presentation shall present a systematic, at the same time visual and mathematically sound, approach to using modular origami polyhedra for teaching point groups using a inquiry-based hands-on approach.

crystallographic point groups; crystal class models; teaching group theory

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