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Mirrors There's more to the Mite than meets the eye. Figure 13-5a shows a corresponding face of both a positive and a negative Mite. As every Mite incorporates both a positive and a negative A-module, it is the unpaired B-module—slanting off to one side or the other—that determines the charge of the overall system. From the above recipe, it appears evident that this minimum space-filling tetrahedron is either right- or left-handed. This was also evident from our initial generating procedure, subdividing the IVM to carve out the smallest repeating unit with mirror symmetry, which is then split into equivalent mirror-image (positive and negative) Mites. However, a surprising and easily overlooked result of joining two A's and a B modifies the above conclusion. An unexpected mirror plane runs through the middle of this irregular tetrahedron that we have assumed must be either right- or left-handed. This means that a Mite is actually its own mirror image. The positive and negative versions are identical. The slanting orientation depicted in Figure 13-5a obscures this fact; however, it turns out that the Mite has two isoceles faces, a fact that indicates that the remaining two faces must be identical (but mirror-image) triangles. Therefore, the outside container of the Mite (ignoring the arrangement of its modular ingredients) incorporates a subtle mirror plane and is actually exactly the same shape as its mirror image. A We can conclude therefore that the two versions are identical; however, Bucky points out that different internal configurations cannot be ignored, for they point to different energy characteristics: Though outwardly conformed identically with one another, the Mites are always either positively or negatively biased internally with respect to their energy valving (amplifying, chocking, cutting off, and holding) proclivities. (954.43) Cubes into Mites Once the A- and B-game gets going, significant relationships are uncovered at every move. The game thus becomes more and more fascinating as it is played. For example, we might carve open a cube, generating six square-based pyramids, one from each face to the cg. Then slice each square pyramid into quarters, like a peanut-butter sandwich. We thereby rediscover the Mite, observing that the cube consists of twenty-four Mites (Fig. 13-6a). Oriented with one of its isosceles triangles (45° -45° -90°) on the cube's surface, the Mite simply rotates to transform Octet Trusses into boxes.
Rhombic Dodecahedra Next, we apply the LCD procedure to the rhombic dodecahedron. Its twelve faces each frame a diamond-shaped valley ending at the cg point. Each of these inverted pyramids can be split into four (two positive, two negative) asymmetrical tetrahedra (Fig. 13-6b). This is the LCD of Fuller's "spheric," and it is none other than the Mite, the LCD of the isotropic vector matrix. Forty-eight Mites in yet another orientation make up this space-filling shape. Not surprisingly, space-filling and Mites have an important connection. No longer caught off guard by such interconnectedness, we conclude by observing that the Mite—faithfully representing octet symmetry—is also an integral component of the cube and the rhombic dodecahedron. Coupler
Fuller's
The equal The other cross-sections ( "Couplers literally couple 'everything'" (954.50). Aptly named, the new octahedron joins together both pairs of cubes and pairs of rhombic dodecahedra. Fuller's nomenclature proves quite logical: We give it the name the Coupler because it always occurs between the adjacently matching diamond faces of all the symmetrical allspace-filling rhombic dodecahedra, the "spherics"...·(954.47) The coupler's different pairs of opposite vertices reach to the geometric centers of two adjacent polyhedra (cube or spheric, depending on the orientation), incorporating their shared face as a cross-section (Fig. 13-8a, b). Half a coupler belongs to one cube (or spheric), and the other half to its neighbor. So the coupler literally couples-well, not "everything" but-a couple of space-fillers.
Fuller continues: The coupler's role is cosmically relevant, for "rhombic dodecahedra are the unique cosmic domains of their respectively embraced unit radius closest-packed spheres" (954.47). The coupler therefore connects the centers of gravity of adjacent spheres, and its domain includes both the spheres and the intervening (dead air) space. This observation explains why the coupler's volumetric center was labeled ... The uniquely asymmetrical octahedra serve most economically to join, or couple, the centers of volume of each of the 12 unit radius spheres tangentially closest packed around every closest packed sphere in Universe, with the center of volume of that omnisymmetrical, ergo nuclear, sphere. (954.48) Perhaps the most intriguing aspect of the coupler is its similar role in the cube and in the rhombic dodecahedron, thereby linking (or coupling) the two space fillers in a new partnership. |

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