I have interests in engineering applied to STEM. Therefore, I am involved in creating objects that have a geometric background with not only educational math content but also industrial applications. They have to be beautiful in order to be appealing to everyone.
3D stars without core. These two star polyhedra come from the symmetry planes of the square cuboid and the cube. On the left, the legs of the 3D star belong to the three planes of symmetry that are parallel to the surfaces and, on the right, the legs belong to six diagonal planes. Furthermore, these 3D stars do not have core (no nucleus) and any leg has ribs going through to the point: on the left, 3D star with 6 legs with point of 4 ribs; on the right 8 legs (6 ribs) and 6 legs (4 ribs). Once we have the supporting polyhedron and a choice of planes with a common center, we can choose a combination of legs with different designs in order to obtain beautiful 3D stars. These features can be extended to parallelepipeds and other polyhedra.