The following post is by Connie Quezada as a part of George Mason University, Math 401, Mathematics through 3D Printing.
Explanation of wallpaper groups:
A Wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on symmetries in the pattern. These patters can be found frequently in architecture and decorative art.
Evgraf Fedorov proved that there are only seventeen distinct groups of possible patterns in 1891.
The symmetry of a pattern is the way of transforming the pattern so that it looks exactly the same after the transformation. Examples of symmetries are translation, reflections, and rotations.
The notation for groups begin with either with p or c for primitive cell or a face-centered cell, then followed by a digit indicating the highest order of rotational symmetry, and the next two symbols indicate symmetries relative to one translation axis of the pattern and are either m for mirror, g for glide reflection, or 1 for none.
My Wallpaper group:
The group pgg contains two rotation centers of order two (180), and glide reflections in two perpendicular directions. There are no reflections and the centers of rotation are not located on the glide reflection axes.
This wallpaper group can be found on Mesopotamian artifacts and is also used as a way of tiling bricks and tiles on roads.
On my print the different colors are used to illustrate the glide reflections being performed on a single tile. When I printed, I printed the original tile and the reflection of the tile with a star design placed on top.
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