Because this post might seem a bit abstract and unconnected to anything on this 2012th Christmas, I have included a link to a most deeply touching story at the end for balance.
The match between the real world Planet Earth and the central sphere of the cubodal form’s ideality presented a sublime metaphor: In an infinite center-less universe, it is still one universe, and because it is one with a distinct beginning, an act of creation is suggested with its Creator at the center of it all.
A more physical connection between our planet and the cuboda is this: earth - like most all celestial bodies – is a spinning sphere with an axis of rotation. So the next step toward a conceptual model is to determine how the cuboda is oriented relative to earth’s poles.
Toward this end, 4 different sets of opposing geometric features characterizing the cuboda’s outer shell present themselves as candidates. That is, opposing pairs of edges, squares, triangles, or vertices. Vertices represent the end points of 12 lines radiating from the cuboda’s natural center, and because these oppose each other exactly in relation to the center, the 12 lines are actually 6, each of which transfixes the central sphere. In the first useful interplay between cubodal expressions, any one line may be selected to coincide with earth’s axis.
Thus designated, the cubodal shell (or spherical anti-entropic thunderhead) is viewed as spinning relative to the earth sphere, such that any of the cuboda’s prime geometric features situated directly out from the equator can be positioned above any longitude, at any time. This maneuver is referred to as primary rotation; and only by orienting opposing vertices to coincide with the earth’s axis can all cubodal features be so positioned.
To further locate features at any latitude (of any longitude), imaginary axes are placed through the center of those opposing features situated directly out from the equator – wherefrom features situated 90˚ from them are rotated via secondary rotations. If this seems highly irregular, a parallel is found in the real and imaginary numbers necessary to grapple with the math of wave dynamics in the realm of physics.
Imaginary axes may be centered through any pair of equatorially opposing features. But another reason for choosing opposing vertices to align with earth’s real poles is that this uniquely orients one (and only one) of the remaining pairs of opposing vertices at the equator, a circumstance that enables equatorial squares to be latitudinally located. Alternatively, the remaining 8 vertices have no distinction from each other and are positioned via secondary rotations about equatorial axes passing through opposing equatorial triangles to guide design of “tree” mounds.)
Thus by real and imaginary axes, primary and secondary rotations may locate features universally. The ability to position features in this manner is important in practice because each feature represents a pattern orientation with its own special applicabilities.
A more sublime aspect of this universality is that it essentially holds all space/time positions on earth to be equal and thus mirrors the notion that as any such perspective represented by an individual soul is unique and part of an incredible variety over the domain of earth, each also holds equal (potential) value to the ultimate Creator of the one universe.
So much for abstraction. If you click on the graphic, you will be taken to a story I heard during a Christmas years ago on NPR. Remembering it days ago, I got so choked up I could hardly describe it to a loved one.