PLA-Tonix - Creative Technologies Capstone
3D Printed Platonic Solids that display Cross Sectional Geometries
During the fall semester of 2022, I worked as a mathematics research assistant with math professor Dr. Jill Cochran at Berry College. In this role, I was able to share my knowledge of 3D printing and web design while also learning about mathematical concepts from calculus, geometry, and algebra.
During a research meeting, the topic of cross sections came up, and Dr. Cochran shared a worksheet that she had showed her math students earlier. The sheet contained a variety of cross section-related puzzles that required students to identify platonic solids based on their cross sections alone. I was thoroughly stumped by the exercise, though it prompted questions of how a teacher could make visualizing cross sections easier for their students. This idea was what prompted me to design PLA-Tonix. Having 3D printed solids with print-in-place hinges would allow students to physically open models and examine their inner cross sections.
PLA-Tonix was named for the material the solids are printed from (PLA) combined with Platonic. Each solid was printed in PLA, with the exception of the tetrahedron, which was printed in PETG.
I began this project with a simple set of parameters: the solids would 1) be easy to print, even for absolute beginners, 2) be easy for users to manipulate, and 3) would display cross sections from more than one angle.
PLA-Tonix consists of a tetrahedron, two octahedrons, a hexahedron, an icosahedron, and a dodecahedron. To make the printing process as easy as possible, every solid has print-in-place hinges and displays 2-3 cross sections each.
These solids were all designed in Fusion 360. Both the octahedron and tetrahedron models feature internal hinges, while the later models have external hinges.
The hexahedron is the most complicated model, with three different cross sections.
Like the hexahedron, the icosahedron has three cross sections. These were colored in using Sharpie paint markers.
Following feedback about the solids' complexity, the dodecahedron was scaled back to include only two cross sections.
These solids were tested by four geometry teachers at Rome High School in Rome, Georgia. Each of them filled out a survey that allowed me to evaluate the state of the solids and determine what needed to be changed.
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