and each ellipsoidal element being characterized by being able to be optionally connected to the first four ellipsoidal elements that have been correctly gravity stacked on the gravity tray in the rectangular or pyramidal configuration, by being considered the fifth ellipsoidal element and being correctly oriented and gravity stacked on top of the first four ellipsoidal elements, so that the second connecting holes of the fifth and first ellipsoidal elements are in alignment, the third connecting holes of the fifth and second ellipsoidal elements are in alignment, the fifth connecting holes of the fifth and third ellipsoidal elements are in alignment and the sixth connecting holes of the fifth and fourth ellipsoidal elements are in alignment, thus allowing optional connection of the fifth ellipsoidal element to any or all of the first four ellipsoidal elements without moving any of the ellipsoidal elements from their gravity stacked positions on the gravity tray.

Thus the plurality of ellipsoids have six unique connector holes similarly located through their centerpoints and have similarly located common axis orientation marks, similarly located triangular or tetrahedron orientation up marks and similarly located rectangular orientation or square pyramidal up marks, where the six connector holes are made in such a manner that the ellipsoidal elements optionally may be connected without disturbing the gravity stacked position of the ellipsoidal elements on the gravity tray when the ellipsoidal elements are gravity stacked properly in either the tetrahedral configuration or the pyramidal (one-half octahedron) configuration.

Alternately the unique connector hole endpoints may be velcro or magnetic elements that have a polarity effect to them as it is seen that the unique connector holes are effectively polarized. For example, it is necessary to have opposite endpoints of the same connector hole touching each other before even the same unique connector holes can be correctly optionally connected. Another method to connect the gravity stacked ellipsoidal elements uses multiple suction cups made of soft rubber or other flexible material on each side of an effective zero length coupling device that optionally can be placed at the contact points as the elements are being gravity stacked.

Table I gives four different types of ellipsoids sets in Sections (a) through (d). It is logical to dimension the ellipsoid sets and their corresponding tetrahedron and octahedron block sets using a method that give similar ratios for similar distances if such a method exists. One such method is to define the center-to- center distance between the first four ellipsoids that can be gravity stacked on the tray in the simple tetrahedron configuration. In Figure 4.2, the said four ellipsoids are 401, 402, 403 and 421. Then use these same center-to-center distances as the corner-to-corner distances between the spacepoints of the corresponding tetrahedrons and octahedrons as shown in Figure 7.0. This causes the distances between spacepoints 701 and 702 to be the same as the distances between centerpoints 401 and 402; between spacepoints 702 and 703 to be the same as between centerpoints 402 and 403; between spacepoints 703 and 701 to be the same as between centerpoints 403 and 401; between spacepoints 721 and 701 to be the same as between centerpoints 421 and 401; between spacepoints 721 and 702 to be the same as between centerpoints 421 and 402; and between spacepoints 721 and 703 to be the same as between centerpoints 421 and 403. This method of dimensioning enables the exact same ratios of distances to be used in Table I Sections (a) through (d) for center-to-center distances for ellipsoids 401, 402, 403 and 421, and in Table II Sections (a) through (d) for corner-to-corner distances for spacepoints 701, 702, 703 and 721 for the corresponding matching 'up' tetrahedron and the corresponding spacepoints for the matching 'down' tetrahedron and the corresponding spacepoints for the matching octahedron as shown in Figure 7.0.