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Next: Columns with Finite Symmetry Up: Columns with Discrete Symmetry Previous: Periodic Columns with No

Discrete Corkscrew Columns -- Five Types

There are three column types having ${\bf N}_\pi$ symmetry. These columns remain the same when translated in the axial direction a unit distance and simultaneously rotated through the angle $180^\circ$ ($\pi/k$ ,in general). Among these columns are those that are invariant under reflection through the centerplane of the column ( ${\bf Z}_2(\kappa)$ ), those that are invariant under reflection through a plane containing the cylinder axis(${\bf Z}_2(\tau)$ )and those that are invariant under both reflections. SeeFigures  1819 and  20.


   
Figure:Corkscrew column with $\pi /2$ rotation and left-right reflection.



   
Figure:Corkscrew column with $\pi /2$ rotation and up-down reflection.



   
Figure:Corkscrew column with $\pi /2$ rotation and left-right and up-down reflections.


There are two continuous families depending on $\omega $ with discrete corkscrew motions (those with ${\bf N}_\omega$ symmetry). See Figures 21 and  22.


   
Figure:Corkscrew column with $\omega $ rotations where $0^\circ\le\omega\le\frac{180^\circ}{k}$ and no additional symmetry.



  
Figure:Corkscrew column with $\omega $ rotations where $0^\circ\le\omega\le\frac{180^\circ}{k}$ and up-down rotation.



next up previous
Next: Columns with Finite Symmetry Up: Columns with Discrete Symmetry Previous: Periodic Columns with No
Marty Golubitsky
2001-01-29