Vibrant Snake Scales

thingiverse

David Lampton 9/10/2021 George Mason University Math 401 Mathematics Through 3D Printing Assignment 1 Hey everyone, I am new to Thingiverse, and I am a college student. I am excited to announce that this is my first thing that I have created. As you can tell, it is a collection of shapes all in the form of a convex pentagon. The convex pentagon shape is one of 15 that can tile the plane monohedrally. (Only one shape type needed) This pentagon shape is of Type 7 (The 7th one to be discovered), and it was discovered by mathematician Richard Kershner in 1968. In pentagon type 7, four sides are of equal length and three angles are equal. Another interesting thing to note about Type 7 is that it has chiral pairs. This means if that if you have a pattern consisting of multiple pairs of shapes, their reflection will be dissimilar in relation to one another and they will not be superimposable. (an object's reflection and the object itself will not preserve the original object's shape when placed on top of one another) When I created this object, I did not use any standard mathematical equations in the coding process aside from a small amount of trigonometry. Instead, I copied a code specific to my pentagon type that my teacher provided me with. It consisted of functions intrinsic to OpenSCAD including scaling and the pentagon function, and the trigonometry was within the scaling function. After scaling and modifying the shape a little to my liking, I decided that the shape reminded me of a snake's scale because it was fat and pointy at the same time. Hence the name snake scales. The OpenSCAD file only contained only one shape, so I used Ultimaker Cura to make copies. When it came time to print, I unfortunately forgot the name of the printer type except that I know it was not the S5. I decided to print the shapes in two colors being purple and green, because I thought those are cool reptile colors. They ended up being blue and green instead, but that is fine as well. The printing process probably took approximately 6 hours to complete. The process was in two parts where I printed 4 shapes in 3 hours each coming to 8 pieces in total. The pieces needed some rafts but no supports. I had one of the supervisors in the print lab see to it that my shapes got printed. I appreciate her help. Overall, thank you for tuning in and I hope you enjoyed reading about my first shape! I am unsure how to fit all the pieces in a pattern right now, but I can follow up if you want to see a future pic of them all together. https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/ https://en.wikipedia.org/wiki/Pentagonal_tiling#CITEREFKershner1968