CPS Geometry

In a plane, spheres can be arranged in a plane in such a way that each ball touches exactly six other balls. This is the hexagonal lattice. In this case, the planes are closer packed than in the square arrangement. But a ball placed in a nest formed by a cluster of three balls does not sink as deep as a ball placed in a nest of a cluster formed by four balls - as we have seen in the square arrangement. As seen previously in the square arrangement, again each ball in the hexagonal arrangement also has exactly twelve neighbors in space. In this there are three balls in the plane below, six balls in the same plane and three balls in the plane above.

In a plane, spheres can be arranged in a plane in such a way that each ball touches exactly four other balls. This is the square lattice. The plane above and the plane below follow the same pattern. The spheres from the second plane fit perfectly in the nests form by four spheres from the first plane. The square pattern is seen better when using struts to connect the nodes.

A sphere can be completely surrounded by exactly twelve others identical spheres. By connecting the spheres with struts, along the directions imposed by close packing of spheres pattern, one ends up with Platonic Structures.