symmetry

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For an introductory-level course, one useful teaching strategy for greater understanding is to regularly make students aware of the connections and symmetries between results established in different parts of the course.
With no exceptions, each crystal was found to conform to one of only 32 ways of combining these symmetry axes, the so-called "crystallographic" point group symmetries.
Besides soccer balls and geodesic domes, other objects ranging from eagelike fullerene molecules and some microorganisms called diatoms to the dice used in games such as Dungeons and Dragons manifest that same set of fivefold, threefold, and twofold symmetries.
The experiment will improve the existing tests of these important fundamental symmetries of nature by a factor of 1000 and should provide tests of various theories of quantum gravity, such as string theory, which predict violations of CPT and Lorentz invariance.