EXERCISE ON CRYSTALLOGRAPHIC BAND GROUPS (“FRIEZE GROUPS”)
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In this exercise, a dolphin was taken as the motif that repeats (itself lacking any symmetry elements within the plane). In a frieze, there is one possible translational symmetry element in addition to the primitive translation; this is the glide. Point symmetry elements that may also occur are the mirror plane and the twofold rotation/centre of inversion. The results are here (use page down or down arrow to scroll through the seven possible friezes): RESULTS.
The same friezes are discussed in more detail in a contribution by Michael Jewess to the Mathematical Gazette: DISCUSSION.
Keywords: crystallography, group theory, frieze group, band group.
Use this link symmetry to contact the author (Dr Michael Jewess).