Aristotle claimed that among the Platonic solids, only regular cubes or regular tetrahedra can tessellate three-dimensional space. In this multivariable calculus project, students investigate whether or not Aristotle was correct!
Students showed that a combination of regular tetrahedra and octahedra can tessellate in three dimensions, and they found something surprising about tetrahedra. They designed some 3D models to demonstrate their findings: a collection of tetrahedra and octahedra, and tetrahedra "dipped" into a sphere to illustrate their approach to the calculations.
| sphwedge.stl | 7.5MB | |
| tessa.stl | 4.0KB | |
| tetra.stl | 284.0B |
