986.400 T Quanta Module

986.401 Consideration 12: Dynamic Spinning of Rhombic Triacontahedron

986.402 I then speculated that the only-by-spinning-produced, only superficially apparent “sphericity” could be roundly aspected by spinning the rhombic triacontahedron of tetravolume 5. This rational volumetric value of exactly 5 tetravolumes placed the rhombic triacontahedron neatly into membership in the primitive hierarchy fainily of symmetric polyhedra, filling the only remaining vacancy in the holistic rational-number hierarchy of primitive polyhedral volumes from 1 through 6, as presented in Table 1053.51A.

986.403 In the isotropic vector matrix system, where R = radius and $P
V = prime vector, *PV =* 1 *=R*ergo, PVR= prime vector radius, which is always the unity ofVE. In the 30-diamond-faceted triacontahedron of tetravolume 5 and the 12-diamond-faceted dodecahedron of tetravolume 6, the radius distances from their respective symmetric polyhedra’s volumetric centers 0 to their respective mid-diamond facesC(i.e., their short-and-long-diamond-axes’ crossing points) are in the rhombic triacontahedral case almost exactly *PVR* i.e.,0.9994833324*PVR*and in the rhombic dodecahedral case exactly *PVR,*1.0000\alpha PVR$.

986.404 In the case of the rhombic dodecahedron the mid-diamond-face point C is exactly PVR distance from the polyhedral system’s volumetric (nucleic) center, while in the case of the rhombic triacontahedron the point C is at approximately PVR distance from the system’s volumetric (nucleic) center. The distance outward to C from the nucleic center of the rhombic dodecahedron is that same $P
VR$ length as the prime unit vector of the isotropic vector matrix. This aspect of the rhombic triacontahedron is shown at Fig. 986.314.

986.405 The symmetric polyhedral centers of both the rhombic dodecahedron and the rhombic triacontahedron may be identified as 0, and both of their respective external diamond faces’ short axes may be identified as A-A and their respective long axes as B-B. Both the rhombic dodecahedron’s and the triacontahedron’s external diamond faces ABAB and their respective volumetric centers 0 describe semiasymmetric pentahedra conventionally labeled as OABAB. The diamond surface faces ABA of both OABAB pentahedra are external to their respective rhombic-hedra symmetrical systems, while their triangular sides OAB (four each) are internal to their respective rhombic-hedra systems. The angles describing the short /-/ axis and the long B-B axis, as well as the surface and central angles of the rhombic dodecahedron’s OABAB pentahedron, all differ from those of the triacontahedron’s OABAB pentahedron.