A further object of the invention is to demonstrate that eight ellipsoids closely packed under the aforementioned four conditions uniquely define two corresponding tetrahedrons plus their corresponding octahedron;

this invention thus demonstrates that two corresponding tetrahedrons plus their corresponding octahedron equal one corresponding rhombohedron;

and it is further shown that each corresponding rhombohedron is equal in volume to six corresponding tetrahedrons;

further still, it is shown that each corresponding octahedron is equal in volume to four corresponding tetrahedrons;

it further demonstrates that the total solid angles of the eight corners of two corresponding tetrahedrons plus the solid angles of the six corners of their corresponding octahedron equal the total solid angle in the centerpoint of one corresponding ellipsoid;

still further, it is shown that there is one general common imaginary thirteen nonparallel plane space latticework that closely packed ellipsoids of influence assume when the aforementioned four conditions are satisfied, where the ellipsoid of influence can be imagined to be in a plurality of ellipsoids in the form of;

(A) a crystal or solid;

(B) a liquid;

(C) a gas; or

(D) very regular helical like spirals of ellipsoids in a radio wave or some other electromagnetic spectrum wave.

Methods that achieve these objects are exemplified by the following methods.

A method teaching the characteristics of corresponding latticework structure comprises the steps of demonstrating the commonality of lattice structure of (a) latticework arranged in accordance with a tetrahedral configuration and (b) latticework arranged in accordance with a pyramidal configuration (one-half octahedron) which has (i) a four-edge base and (ii) four faces that extend from the base and meet at a point, the demonstrating step including the steps of: positioning a plurality of structural members relative to each other to define spacepoints in a latticework arranged in accordance with the tetrahedral configuration; positioning a plurality of structural members relative to each other to define spacepoints in a latticework arranged in accordance with the pyramidal configuration; wherein the positioning steps include merging together structural members along at least one face of the latticework arranged in accordance with the tetrahedral configuration with structural members along at least one corresponding face of the latticework arranged in accordance with the pyramidal configuration to make the spacepoints along at least one tetrahedral face coexistent with the spacepoints on at least one corresponding pyramidal face. Each positioning step includes the step of gravity stacking a plurality of at least substantially similarly dimensioned similarly oriented ellipsoidal elements, wherein each ellipsoidal element is one of the structural members and the centerpoint of each ellipsoidal element is a spacepoint in the latticework.

The educational device of the invention is exemplified by a device for teaching characteristics of latticework structure comprising; a plurality of similarly dimensioned ellipsoidal elements, each ellipsoidal element being dimensionally characterized by a major axis and two minor axes where the axes are orthogonal and are axes of symmetry;

and each ellipsoidal element being characterized by having one end of the common axis marked with a circle or other indicia to indicate the orientation of the common axis;

and each ellipsoidal element being characterized by a common axis connector hole passing through the centerpoint of this common axis orientation mark and the centerpoint of the ellipsoidal element and through the ellipsoidal element and thus uniquely defining the common axis of the ellipsoidal element;

and each ellipsoidal element being characterized by a triangular orientation mark or indicia on the surface of the ellipsoidal element locating the up direction when a first ellipsoidal element is gravity stacked on the gravity tray starting in the tetrahedral configuration;

and each ellipsoidal element being characterized by optionally being capable of being connected to a second ellipsoidal element along their common axis connector holes when both ellipsoidal elements have been gravity stacked on the gravity tray and oriented so that their orientation marks all point the same way with the common axis orientation mark pointing away from the lowest corner of the gravity tray, without being moved from their gravity stacked positions by using a special connecting tool and special torsion spring friction coupling;