Classification of Columns

 

The results of the previous section show that there are twenty-nine symmetry classes of columns. The symmetry class of a column can be determined by answering a sequence of questions. The most important question is:

Are the symmetries of the column continuous, discrete and infinite, or finite?

The column has continuous symmetries when the column can be slid along itself. These symmetries can occur either using either axial translations or rotations about the axis, or by a combination of the two. With two exceptions infinite discrete symmetry groups occur when the column is axially periodic but has no continuous symmetries. Both of the first two types of symmetry groups are infinite. If the symmetry group of a column is not infinite, then it is finite.