Tetrahedron-in-the-box & Stellated Octahedron (also fits in the box)

thingiverse

This model features a box and lid forming a cube shape with an internal space in the same form, plus a regular tetrahedron sized according to the diagonal of any face within the box's inner cube. The tetrahedron fits when its edge aligns diagonally with the base. This demonstrates that the vertices of a regular tetrahedron can be determined by the endpoints of two perpendicular diagonals from opposite sides of the cube. The edge length of the tetrahedron is identical to the diagonal of the internal cube's face. As the simplest solid with plane faces, the regular tetrahedron and cube are classified as 'plutonic solids,' while the sphere stands as the simplest regular solid. This model also highlights that the tetrahedron can be parallel projected along the axis of two opposing edges' centers to form a square. A stellated octahedron, or 'stella octangula,' is included in this design; it consists of two combined tetrahedrons rotated 90 degrees around a central axis and fits within the same box due to equal size. The enclosed cube and tetrahedron boast 2mm thick walls, and printing multiple tetrahedrons at once can prevent distortion caused by rapid top point printing. Ensure good bed adhesion when printing the stellated octahedron, or use a brim feature if available in your slicer software.