Polyhedra.

People frequently encounter objects in polyhedral shapes, such as buildings that have cubic or prismatic shapes and geodesic domes or dice that are shaped like polyhedra. This prevalence is partly because of their aesthetic appeal and partly because of their practical properties. Polyhedra also appear in nature; many crystals have the shapes of regular solids, particularly of tetrahedron, cube, and octahedron, and virus capsids can be icosahedral. Furthermore, carbon atoms can form a type of molecule known as “fullerenes,” which are in the form of a triangulated truncated icosahedron. A polyhedron is a solid in space with polygonal faces that are joined along their edges. If the faces consist of regular polygons, then it is called a “regular polyhedron.” A polyhedron is convex if the line segment joining any two points lies on or inside it. Regular convex polyhedra are particularly important for their aesthetic value, symmetry, and simplicity. There are only five of them: the tetrahedron, cube or hexahedron, octahedron, dodecahedron, and icosahedron. Beginning in primary school, students investigate and classify geometric shapes, including polyhedra. In middle school and high school, students explore area and volume measurements as well as transformations and cross-sections.