Octagon with Stars (p4m, 2 tiles) by thocal

Last crawled date: 3 years, 4 months ago

Octagon with Stars (p4m, 2 tiles)
Thomas Calderon
George Mason University MATH 401
Mathematics Through 3D Printing
This is my assignment for Mathematics through 3D printing at George Mason University. My assignment was to create a wallpaper pattern that tiles the plane, using the wallpaper group: p4m. The wallpaper group p4m is different than other groups in that it requires two tiles to cover the plane.
Taking a step back, there are a total of 17 groups that tile the plane. This was proven in 1891, by Evgraf Fedorov. The wallpaper groups are categorized by their symmetries. The group p4m has two rotation centers of order four (90°), and reflections in four different directions (horizontal, vertical, and diagonal). It also has glide reflections where the axes are not reflection axes and rotations of order two (180°) which are centered at the intersection of the glide reflection axes. All rotation centers are on reflection axes.
As you can see, I used two patterns in the pictures provided. There is an octagon and a star shape that fits inside the spaces between the octagons (two distinct tiles). I decided to use these two patterns because they complemented each other naturally and made it easier for me to make. In addition, I had to make my octagons overlap, creating a never ending octagon pattern. I will admit I am new to this type of coding, so my code may be lengthy. I would appreciate any suggestions on how to make my coding more concise in the future.
https://en.wikipedia.org/wiki/Wallpaper_group#Group_p4m_(*442)http://dubath.net/tiling/exemples_en.htmlhttp://math.hws.edu/eck/js/symmetry/wallpaper.html