P3m1 Wallpaper Group

George Mason University Math 401 Mathematics Through 3D Printing Jean-Marc Daviau-Williams

My wallpaper group was the p3m1 configuration. The parameters for this wallpaper group are three points of rotation, which all must lie on mirror lines, hence must have a reflection. For my design (which was made using this application) I chose to compose my tiling using equilateral triangles with three different designs in two colors. The first color was yellow that was a plain triangle with no design. For the other two triangles, I made them red with two designs. One had a single line passing through a vertex and its opposite side and the other had three lines passing through in the same manner. Through this, I was able to achieve the requirement for the p3m1 wallpaper group.

The process of making the 3D model was done OpenSCAD in three parts, in two files. First, I created a two .scad files, placing a single equilateral triangle with a small height, and then two equilateral triangles in the second with the same configuration. Next, I made a rectangular prism and smaller equilateral triangle and have it start at a vertex and travel to its opposite side. Finally, on the last triangle in the second file, I copied that same shape and rotated it 60 degrees for the two copies, adjusting their position accordingly.

As for the print itself, I printed the object over the course of a couple of hours with the Makerbot, which would take less time to build as opposed to some of the other printers in the GMU MakerLab, as the switching of colors is easy to do and my design was not intricate. However, it did require the construction of a large, ugly, and hard-to-remove raft to be constructed as a support first which padded on to the build time. An improvement I would make in the future is to break down my .scad code into more manageable modules, as adjusting for the shape's rotation was difficult and messy.

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