Question

Proof volume is cut into two equal halves by any plane through the center of symmetry

Answer 1





The formulation of the problem is somewhat misleading. For someone who does not work with polyhedra on a daily basis the word octahedronwill probably emerge as the center of attraction, as the main piece of data that required most of one's attention. Octahedron is one of the five Platonic bodies. These are regular polyhedra, i.e. polyhedra such that at any vertex the same number of faces meet and, in addition, all faces are formed by equal regular polygons. Octahedron has 8 faces, 12 edges and 6 vertices. There is a special symmetry octahedral group named after this shape. In particular, octahedron possesses central symmetry. In other words, there exists a point O such that the octahedron is symmetric with respect to that point.