Next: Discrete Corkscrew Columns Up: Columns with Discrete Symmetry Previous: Columns with Discrete Symmetry Periodic Columns with No Corkscrew Symmetry -- Eight TypesRecall that
is a reflection through a plane containing the axis of the cylinder and
is the reflection through the midplane - the up-down symmetry. Each of these
symmetries has a glide reflectionversion There are ten subsets that form symmetry groups when coupled with .These subsets are: The symmetry groups of the corresponding periodic columns are: --the group generated by G and .Examples of columns having one purereflection symmetry are found in Figures 10and 11. Examples of columns having precisely one glide reflection are given inFigures 12 and 13. Columns having two reflections or glidereflections are shown in Figures 14,15, 16 and 17. The last two subsets correspond to symmetry groups that lie in infinite families and these infinite families have corkscrew symmetries (see Figures 21and 22).
Next: Discrete Corkscrew Columns Up: Columns with Discrete Symmetry Previous: Columns with Discrete Symmetry Marty Golubitsky 2001-01-29 |