The initial assemblage of spheres in Elements of Space was easy enough, but to avoid the pitfall of endless disorder resulting from indiscriminate deep-nesting of the next few spheres, how would we proceed?  

The a posteriori answer is to place forthcoming spheres by means of rational accretion, a term borrowed from the field of astrophysics to denote the process of celestial body-building. Actually, rational accretion began when relative sphere size and positions were specified.

The initial 4 placements might have been called "idealized symbolic accretion" by virtue of principles engaged - like equality and the conduct of neighborly contact, with good (spherical surface) fences perhaps symbolizing mutual respect (R. Frost).

To proceed, the 4-sphere tetrahedral cluster is scrutinized:

Its spheres can easily be regarded as 2 pairs of spheres. In focusing on the lines joining the centers of the 2 spheres comprising each pair, they appear to cross and symmetrically organize the space around them into 4 equivalent areas. From this perspective, the idea of right angle orthogonality emerges.

With the right angle idea in mind, sphere 5 is not deep-nested, but rather planar-nested between spheres, one from each pair, so as to form an actual right angle. Then by placing sphere 6 similarly next to sphere 5, a complete circuit of real right angles forms a square.

Two key observations regarding the now 6-sphere cluster are: only 1 sphere is now in contact with every other sphere; of those 5 other spheres, the square and triangular clusters they form share 2 spheres, as well as the common line joining those spheres' center-points.

This common border between plane types and the emergence of one common sphere suggest central organization and some pattern for new placements to follow in The Cuboda, topic 3 of Orientation.