Border Order - 1

There are so many border rangOlis I see nowadays. This one and the next one in this
series explains the mathematical order in the borders. Borders are basically one
dimensional. Only two-fold rotations (180 degree rotations) are considered herein.
Vertical and horizontal mirrors are also considered. Also translations, that is,
movements along the border length after a reflection in the horizontal mirror are
also considered. Such movements after a reflection are called glides.
In this picture, four are considered -
(1) No symmetry, (2) a glide (reflection followed by translation, i.e., movement along
the border direction), (3) A two-fold rotation (180 deg rotation), (4) vertical mirror.

Regards! - mOhana