Concentric Shell Growth Rates
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415.00
Concentric Shell Growth Rates
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415.01
Minimal Most Primitive Concentric Shell Growth Rates
of Equiradius,
Closest-Packed, Symmetrical Nucleated Structures: Out
of all possible symmetrical
polyhedra produceable by closest-packed spheres agglomerating,
only the vector
equilibrium accommodates a one-to-one arithmetical progression
growth of frequency
number and shell number developed by closest-packed,
equiradius spheres around one
nuclear sphere. Only the vector equilibrium__"equanimity"__accommodates
the
symmetrical growth or contraction of a nucleus-containing
aggregate of closest-packed,
equiradius spheres characterized by either even or odd
numbers of concentric shells.
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415.02
Odd or Even Shell Growth: The hierarchy of progressive
shell
embracements of symmetrically closest-packed spheres
of the vector equilibrium is
generated by a smooth arithmetic progression of both
even and odd frequencies. That is,
each successively embracing layer of closest-packed
spheres is in exact frequency and shell
number atunement. Furthermore, additional embracing
layers are accomplished with the
least number of spheres per exact arithmetic progression
of higher frequencies.
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 Chart 415.03 |
415.03
Even-Number Shell Growth: The tetrahedron, octahedron,
cube, and
rhombic dodecahedron are nuclear agglomerations generated
only by even-numbered
frequencies:
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415.10
Yin-Yang As Two (Note to Chart 415.03): Even at zero
frequency of the
vector equilibrium, there is a fundamental twoness that
is not just that of opposite polarity,
but the twoness of the concave and the convex, i.e.,
of the inwardness and outwardness,
i.e., of the microcosm and of the macrocosm. We find
that the nucleus is really two layers
because its inwardness tums around at its own center
and becomes outwardness. So we
have the congruence of the inbound layer and the outbound
layer of the center ball.
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415.11
When they finally learned that the inventory of data
required the isolation of
the neutron, they were isolating the concave. When they
isolated the proton, they isolated
the convex.
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415.12
As is shown in the comparative table of closest-packed,
equiradius nucleated
polyhedra, the vector equilibrium not only provides
an orderly shell for each frequency,
which is not provided by any other polyhedra, but also
gives the nuclear sphere the first,
or earliest possible, polyhedral symmetrical enclosure,
and it does so with the least
number__12 spheres; whereas the octahedron closest packed
requires 18 spheres; the
tetrahedron, 34; the rhombic dodecahedron, 92; the cube,
364; and the other two
symmetric Platonic solids, the icosahedron and the dodecahedron,
are inherently, ergo
forever, devoid of equiradius nuclear spheres, having
insufficient radius space within the
triangulated inner void to accommodate an additional
equiradius sphere. This inherent
disassociation from nucleated systems suggests both
electron and neutron behavior
identification relationships for the icosahedron's and
the dodecahedron's requisite
noncontiguous symmetrical positioning outwardly from
the symmetrically nucleated
aggregates. The nucleation of the octahedron, tetrahedron,
rhombic dodecahedron, and
cube very probably plays an important part in the atomic
structuring as well as in the
chemical compounding and in crystallography. They interplay
to produce the isotopal
Magic Number high point abundance occurrences. (See
Sec. 995.)
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415.13
The formula for the nucleated rhombic dodecahedron
is the formula for the
octahedron with frequency plus four (because it expands
outwardly in four-wavelength
leaps) plus eight times the closest-packed central angles
of a tetrahedron. The progression
of layers at frequency plus four is made only when we
have one ball in the middle of a
five-ball edge triangle, which always occurs again four
frequencies later.
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415.14
The number of balls in a single-layer, closest-packed,
equiradius triangular
assemblage is always
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415.15
To arrive at the cumulative number of spheres in the
rhombic dodecahedron,
you have to solve the formula for the octahedron at
progressive frequencies plus four, plus
the solutions for the balls in the eight triangles .
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415.16
The first cube with 14 balls has no nucleus. The first
cube with a nucleus
occurs by the addition of 87-ball corners to the eight
triangular facets of a four-frequency
vector equilibrium.
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 Fig. 415.17 |
415.17
Nucleated Cube: The "External" Octahedron: The minimum
allspace-
filling nuclear cube is formed by adding eight Eighth-Octahedra
to the eight triangular
facets of the nucleated vector equilibrium of tetravolume-20,
with a total tetravolume
involvement of 4 + 20 = 24 quanta modules. This produces
a cubical nuclear involvement
domain
(see Sec. 1006.30)
of tetravolume-24: 24 × 24
= 576 quanta modules.
(See Sec. 463.05
and Figs. 415.17A-F.)
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415.171
The nuclear cube and its six neighboring counterparts
are the volumetrically
maximum members of the primitive hierarchy of concentric,
symmetric, pre-time-size,
subfrequency-generalized, polyhedral nuclear domains
of synergetic-energetic geometry.
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415.172
The construction of the first nuclear cube in effect
restores the vector-
equilibrium truncations. The minimum to be composited
from closestpacked unit radius
squares has 55 balls in the vector equilibrium. The
first nucleated cube has 63 balls in the
total aggregation.
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| Next Section: 415.20 |