With the rise of personal desktop 3D printing, a wide spectrum of educational opportunities has become available for educators to leverage this technology in their classrooms. Until recently, the ability to create physical 3D models was well beyond the scope, skill, and budget of many schools. However, since desktop 3D printers have become readily…

Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

In this paper, results from a subset of the Purdue Spatial Visualization Test and a self-efficacy test developed by the authors are presented to determine whether certain object shapes, orientations, and types of rotations in standard spatial ability tests cause more difficulty than others and whether a solid object, which includes shading to…