Cutting Edge > Mineralogy > Crystal Symmetry Through Dance > Symmetry and Old Time Dancing

Symmetry and "Old Time Dances"

Traditional "old time" or country dances incorporate a large number of symmetry elements in their dance forms. In crystallography, and in "old-time" dancing, most symmetry elements (rotation axes, mirrors, center of symmetry) have been successfully completed if all the atoms (dancers) occupy the same positions before and after the operation. Some symmetry operations involve a translation (glide planes or screw axes) in which case the atomic/dance positions are replicated at a prescribed distances and directions from the original position. In this exercise, we will use a dance set as a metaphor for a crystal structure, and we will illustrate the locations of the symmetry elements as they appear throughout the dance form:
The lattice Pg, showing a glide plane, and considering male (square) and female (circle) positions as being unique. This is the starting configuration for an "improper" contra dance.
The lattice Pm, showing the left side mirrored to the right (male=female). This is the configuration for the "proper" triplet dance.
The P4mm lattice, showing the positions of symmetry elements represented in the square dances.

Look for these symmetry elements in the following demonstration videos. Allow us a bit of artistic, creative license as we use these dance forms to demonstrate symmetry operations. Enjoy the dances, and try them out yourself!

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