It is an object of the invention to demonstrate to a student that given a plurality of ellipsoids of influence closely packed under the following four conditions;

(a) ellipsoids of essentially equal size and shape;

(b) oriented with a similar bearing;

(c) stacked under the influence of gravity;

(d) with at least one common axis;

then:

(I) the latticework structure started with four ellipsoids in a simple tetrahedral configuration; is equal to

(II) the latticework structure started with five ellipsoids in a simple pyramidal or one-half octahedral configuration; is equal to

(III) the latticework structure started with thirteen ellipsoids in a simple cuboctahedral configuration;

when these simple latticework structures of ellipsoids of influence are extended into space.

That is, notwithstanding the fact that the base of the simple tetrahedron latticework structure has a triangular base, the base of the simple octahedron latticework structure has a rectangular base (one-half octahedron), and the simple cuboctahedron latticework structure could be said to have both triangular bases and rectangular bases, the present invention demonstrates that, over space, ellipsoids of influence, arranged by starting in either of the three simple patterns, given the four conditions, closely pack in the same way.

Further, it is an object of the invention to show that a large tetrahedral configuration formed of, for example, ellipsoids, comprises the same internal latticework structure as a large pyramidal (one-half octahedron) configuration formed of the same ellipsoids, and that both of these configurations comprises the same internal latticework structure as a large cuboctahedral configuration formed of the same ellipsoids.

It is yet another object of the invention to demonstrate that in (a) a tetrahedral configuration having a base, or face, of fifteen ellipsoids (e.g. five ellipsoids along each edge) and (b) a pyramidal configuration having a base of twenty-five ellipsoids in a 5 x 5 arrangement, the same 13-ellipsoid cuboctahedral type of configuration is embodied in each. Moreover, in that the cuboctahedral type of configuration of closely packed ellipsoids is common to both the tetrahedral and octahedral configurations, a student will recognize the commonality of latticework structure of the three 'heretofore different' latticeworks, when these latticework structures are extended into space under the influence of gravity.

It is thus a further object of the invention to demonstrate the commonality of the closely packed tetrahedral, octahedral and cuboctahedral configurations of ellipsoids by selectively assembling or disassembling (a) a tetrahedral configuration of ellipsoids and (b) an octahedral configuration of ellipsoids with an intact cuboctahedral type of configuration of closely packed ellipsoids contained therein.

Furthermore, it is an object of the invention to show that the tetrahedral configuration closely packed and expanded into space under the aforementioned four conditions define imaginary thirteen nonparallel planes.

Still further, where a latticework is defined by spacepoints that are determined by the centerpoints of ellipsoids, or other corresponding structural members representing fields of influence that are closely packed under the aforementioned four conditions, then the relative dimensions of the major and minor axes of the ellipsoid when the common axis and the location of either orientation mark are known, uniquely determine the relative distances or lengths between the spacepoints in the corresponding latticework structure.

Conversely, the relative distances or lengths between the four corners of a corresponding tetrahedron, when the edge that is on the common axis is known, uniquely determine the major and minor axes and the location of both orientation marks of the corresponding ellipsoid or ellipsoidal field of influence that creates the corresponding latticework structure and uniquely determine the relative distances or lengths between, and orientation of, the six corners of the corresponding octahedron and uniquely determine the relative distances or lengths between, and orientation of, the four corners of the other inverted corresponding tetrahedron.

Further still, when the common axis and the location of either orientation mare are known, the lengths of the major and minor axes of the corresponding ellipsoid or ellipsoidal field of influence, uniquely define imaginary thirteen nonparallel planes in the corresponding latticework structure when the corresponding ellipsoids are gravity stacked under the aforementioned four conditions.