CM Tile Pattern with Lemniscate

Vincent Vu
September 20, 2021
George Mason University MATH 401: Mathematics Through 3D Printing

This print is of a cm wallpaper group pattern that tiles the xy-plane. For centuries, mathematicians have been searching for tessellations, which is when a repeated pattern filles the plane without any gaps. There are seventeen distinct wallpaper groups that tile the plane, and each of them belongs to their own symmetry group. Symmetry groups are defined by their transformations, which include translations, reflections, and glide reflections. I was assigned Symmetry group 5, or cm wallpaper group, and used OpenSCAD to design my tile.


The cm wallpaper group only has a glide reflection, which means that the figure is translated before being reflected. A good example of a glide reflection is a trail of footprints (assuming a person’s feet are mostly similar). The tile itself was created using OpenSCAD’s polygon() function, and every points besides the tip and the bottom of the poly