TOPOLOGICAL SOLUTION TO THE CYLINDRICAL EINSTEIN–MAXWELL EQUATIONS

A new exact solution to the cylindrically symmetric Einstein–Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be interpreted as a charged domain wall shell.

New types of space-filling polyhedra with fourteen faces

A study of the staggered packing of identical hexagonal prisms leading to four-connected periodic structures with polyhedral cells of fourteen faces has been undertaken. Special attention was given to those packings that lead to periodic structures with two polyhedra per lattice point, and such that the two polyhedra are related by a pure rotation and/or enantiomorphism. The general solution for packings of this type was obtained and the topology of the intervening polyhedra was determined. It is shown that polyhedra with eight hexagonal faces and six square faces, topologically isomorphic to the truncated octahedron, can be packed with or without a rotation. The polyhedra which can be packed with the respective enantiomorphs (with or without rotation) have four square faces, four pentagonal faces and six hexagonal faces. Each type of packing is compatible with Bravais lattices of any category and each topological solution is compatible with a range of convex shapes.