Hypothetical six-dimensional topology.

Although the hypothesis of a six-dimensional spacetime with SO(3,3) symmetry has been investigated by several scholars for over four decades, the related topological analysis still seems inadequate. We propose the Inherently Spinning Spacetime (ISST) as proper background for any 6D geometrodynamics based on the three-dimensional time. The ISST is an axiomatization of the General Relativity manifold where each event is characterized by its own spin angular velocity as additional property. If each point of the continuum is a structureless rotating sphere of null radius, the orientation of its spinning axis is defined by two parameters interpreted as timelike extra-dimensions.