Additional Spatial Dimensions
In addition to the standard 'x' (left/right), 'y' (forward/back), and 'z' (up/down) coordinates, any mathematically consistent depiction of the Manifold would include 'v' (movement between tesseracts) and 'w' (movement between cubes) coordinates. These coordinates occupy axes perpendicular to all others, though physical beings cannot generally percieve them as such.
Within the many cubes of the Manifold Sky, almost all physical (baryonic) objects and forces interact with one another as though the additional spatial dimensions beyond the known three do not exist. For example, circumvection only moves air about in ways appropriate for seasonal variations in temperature, humidity, and the like. What is less apparent, however, is that the extra spatial dimensions conceal adjacent physical spaces, those being other cubes within the same or different tesseracts. For example, while a person in Voxelia might percieve their environment to be an open street corner on a quiet abnemi afternoon, a person in the municipality Petalcap Vale might actually be standing in exactly the same 'x,' 'y,' and 'z' coordinates in space. The difference between these two people is that they are standing 'v' (different tesseract) and 'w' (different cube) distances apart, and, thus, cannot physically interact with one another despite sharing the same location within their own cubes. For reasons unknown, the commissures and inflection layers exist and allow three dimensional beings to cross these hidden dimensions in select locations. Furthermore, certain forces (i.e. gravity) and particles (i.e. photons) are actually able to cross the gaps from without the Manifold or between different regions of the Manifold. This is the way in which, for example, the celestial cycles of day and night and the seasonal polarity changes in the charged particle radiation between the Northern Tesseract and Southern Tesseract are able to occur without apparent causes within the Manifold proper. Physicists working at the Voxelia Academy of Sciences have posited that these particles might be able to cross the otherwise impassible barriers through some sort of 'tunneling,' some sort of probabilistic effect which only applies to very tiny or massless objects and certain forms of energy.
- The Geometries of the Manifold Sky - A History - an explaination for how the the habitable dimensions of the Manifold Sky look as percieved by three-dimensional entities.