¶ Octahedron: Eighth-Octahedra
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RBF Definitions
Octahedron: Eighth-Octahedra:
“By internally interconnecting its six vertexes with three polar axes: X, Y, and Z, and rotating the octahedron successively upon those three axes, three planes are internally generated that symmetrically subdivide the octahedron into eight uniformly equal, equiangle-triangle-based, asymmetrical tetrahedra, with three convergent, 90-degree-angle-surrounded apexes, each of whose volume is one-eighth of the volume of one octahedron: this is called the Eighth-Octahedron. (See also 912.00912. The octahedron having a volume of four tetrahedra, allows each Eighth-Octahedron to have a volume of one-half of one tetrahedron. If we apply the equiangled-triangular base of one each of these eight Eighth-Octahedra to each of the vector equilibrium’s eight equiangle-triangle facets, with the Eighth-Octahedra’s three-90-degree-angle-surrounded vertexes pointing outwardly, they will exactly and symmetrically produce the 24-volume, nucleus-embracing cube symmetrically surrounding the 20-volume vector equilibrium; thus with 8 x 1/2 = 4 being added to the 20-volume vector equilibrium producing a 24-volume total.”
¶ Cross-References
- Sec. 912
¶ Citations
