Fluted Columns -- Two Types

All remaining symmetry groups have at least ${\bf Z}_k$ symmetry for some k,that is, rotation symmetry through an angle $2\pi/k$ .In our description of this classification we now set k=1 with the understanding that there is a version of each of the remaining columns for each natural number k.Indeed, the pictures we show all have k =2.

There are two types of columns with axial translation symmetry: those which have a plane of reflection across a plane containing the axis of the cylinder (${\bf D}_2\dot{+}{\bf R}$ )and those that do not (${\bf Z}_2\dot{+}{\bf R}$ ).See Figures 6 and  7.

   

Figure 6:Fluted column with no left-right reflection.

   

Figure 7:Fluted column with left-right reflection.