430.02 It is called the
vector equilibrium because the radials and the cir-
cumferentials arc all of the same dimension and the tendencies to both ex-
plode and implode are symmetrical. That the explosive and implosive forces
are equal is shown by the four-dimensional hexagonal cross sections whose
radial and circumferential vectors balance. The eight triangular faces reveal
four opposite pairs of single-bonded tetrahedra in a positive
and negative
tetrahedral system array with a common central vertex and with coinciding
ra-
dial edges. The four hexagonal planes (hat cross each other at the center of
the
vector-equilibrium system are parallel to the four faces of each of its eight
tetrahedra. Six square faces occur where the six half-octahedra converge
around the common vector-equilibrium nuclear vertex.
430.03 In terms of vectorial
dynamics, the outward radial thrust of the
vector equilibrium is exactly balanced by the circumferentially restraining
chordal forces: hence the figure is an equilibrium of vectors. All the edges of
the figure are of equal length, and this length is always the same as the dis-
tance of any of its vertexes from the center of the figure. The lines of force
radiating from its center are restrainingly contained by those binding inward
arrayed in finite closure circumferentially around its periphery-barrel-hoop-
ing. The vector equilibrium is an omnidirectional equilibrium of forces in
which the magnitude of its explosive potentials is exactly matched by the
strength of its external cohering bonds. If its forces are reversed, the magni-
tude of its contractive shrinkage is exactly matched by its external compres-
sive archwork's refusal to shrink.
430.04 The vector equilibrium
is a truncated cube made by bisecting the
edges and truncating the eight corners of the cube to make the four axes of the
four planes of the vector equilibrium. The vector equilibrium has been called
the "cuboctahedron" or "cubo-octahedron" by
crystallographers and geo-
meters of the non-experimentally-informed and non-cnergy-concerned past.
As such, it was one of the original 23 Archimedean "solids,"
430.05 The vector equilibrium
is the common denominator of the tetrahe-
dron, octahedron, and cube. It is the decimal unit within the octave system.
Double its radius for octave expansion.
430.06 The vector equilibrium
is a system. It is not a structure. Nor is it a prime volume, because it has a nucleus. It is the prime nucleated system. The eight tetrahedra and the six half-octahedra into which
the vector equilibrium
may be vectorially subdivided are the volumes that are relevantly involved.
440.00
Vector Equilibrium as Zero Model
440.01Equilibrium between positive and negative is zero. The vector
equilibrium is the true zero reference of the energetic mathematics. Zero pul-
sation in the vector equilibrium is the nearest approach we will ever know to
eternity and god: the zerophase of conceptual integrity inherent in the
positive
and negative asymmetries that propagate the differentials of consciousness.
440.02 The vector equilibrium
is of the greatest importance to all of us
because all the nuclear tendencies to implosion and explosion are reversible
and are always in exact balance. The radials and the circumferentials are in
balance. But the important thing is that the radials, which would tend to
explode since they are outwardly pushing, are always frustrated by the tensile
finiteness of the circumferential vectors, which close together in an orderly
manner to cohere the disorderly asundering. When the radial vectors are
tensilely contractive and separately implosive, they are always prevented from
doing so by the finitely closing pushers or compressors of the circumferential
set of vectors. The integrity of Universe is implicit in the external
finiteness of
the circumferential set and its surface-layer, close-packing,
radius-contracting
proclivity which always encloses the otherwise divisive internal radial set of
omnidirectional vectors.
440.03 All the internal, or
nuclear, affairs of the atom occur internally to
the vector equilibrium. All the external, or chemical, compoundings or asso-
ciations occur externally to the vector equilibrium. All the phenomena exter-
nal to-and more complex than-the five-frequency vector equilibria relate to
chemical compounds. Anything internal to-or less complex than-the five-
frequency vector equilibrium relates principally to single atoms. Single atoms
maintain omnisymmetries; whereas chemical compounds may associate as
polarized and asymmetrical chain systems.
440.04 The vector equilibrium
is the anywhere, anywhen, eternally re-
generative, event inceptioning and evolutionary accommodation and will
never be seen by man in any physical experience. Yet it is the frame of
evolvement. It is not in rotation. It is sizeless and timeless. We have its
math-
ematics, which deals discretely with the chordal lengths. The radial vectors
and circumferential vectors are the same size.
440.05 The vector equilibrium
is a condition in which nature never allows
herself to tarry. The vector equilibrium itself is never found exactly
symmetri-
cal in nature's crystallography. Ever pulsive and impulsive, nature never
pauses her cycling at equilibrium: she refuses to get caught irrecoverably at
the zero phase of energy. She always closes her transformative cycles at the
maximum positive or negative asymmetry stages. See the delicate crystal
asymmetry in nature. We have vector equilibriums mildly distorted to asym-
metry limits as nature pulsates positively and negatively in respect to
equilib-
rium. Everything that we know as reality has to be either a positive or a nega-
tive aspect of the omnipulsative physical Universe. Therefore, there will
always be positive and negative sets that are ever interchangeably intertrans-
formative with uniquely differentiable characteristics.
440.06 The vector equilibrium
is at once the concentric push-pull in-
terchange, vectorial phase or zone, of neutral resonance which occurs be-
tween outwardly pushing wave propagation and inwardly pulling gravitational
coherence.
440.07 All the fundamental
forms of the crystals are involved in the vec-
tor equilibrium. It is a starting-point-not anything in its own right-if it is
a
vector equilibrium.
440.08 As the circumferentially united and finite great-circle chord vec-
tors of the vector equilibrium cohere the radial vectors, so also does the
meta-
physical cohere the physical.
441.00
Vector Equilibrium as Zero Tetrahedron
441.01Emptiness at the Center: All four planes of all eight tetrahe-
dra, i.e., 32 planes in all, are congruent in the four visible planes passing
through their common vector equilibrium center. Yet
you see only four
planes. Both the positive and the negative phase of the tetrahedra are in
congruence in the center. They are able to do this because they are synchro-
nously discontinuous. Their common center provides the locale of an abso-
lutely empty event.
441.02 Vector equilibrium
accommodates all the intertransformings of
any one tetrahedron by polar pumping, or turning itself inside out. Each vec-
tor equilibrium has four directions in which it could turn inside out. It uses all
four of them through the vector equilibrium's common center and generates
eight tetrahedra. The vector equilibrium is a tetrahedron exploding itself,
turn-
ing itself inside out in four possible directions. So we get eight: inside and
outside in four directions. The vector equilibrium is all eight of the
potentials.
443.00
Vector Equilibrium as Equanimity Model
443.01 In order to reduce the
concept of vector equilibrium to a single-
name identity, we employ the word equanimity as identifying the eternal
metaphysical conceptuality model that eternally tolerates and accommodates
all the physically regenerative intertransforming
transactions of eternal, inex-
orable, and irreversible evolution's complex complementations, which are
unitarily unthinkable, though finite.
443.02 The equanimity model
permits metaphysically conceptual think-
ability and permits man to employ the package-word Universe. Equanimity,
the epistemological model, is the omni-intertransformative, angle- and
frequency-modulatable, differential accommodator and identifies the direction
toward the absolute, completely exquisite limit of zero-error, zero-time om-
nicomprehension toward which our oscillatory,
pulsating reduction of tol-
erated cerebrally reflexed aberrations trends.
443.03 Humanity's physical
brains' inherent subjective-to-objective time
lag reflexing induces the relatively aberrated observation and asymmetrical ar-
ticulation tolerated by ever more inclusively and incisively demanding mind's
consciousness of the absolute exactitude of the eternally referential
centrality
at zero of the equanimity model. Thus mind induces human consciousness
of
evolutionary participation to seek cosmic zero. Cosmic zero is conceptually
but sizelessly complex, though full-size-range accommodating.
443.04 In the equanimity
model, the physical and the metaphysical share
the same design. The whole of physical Universe experience is a consequence
of our not seeing instantly, which introduces time. As a result of the gamut of
relative recall time-lags, the physical is always the imperfect experience, but
tantalizingly always ratio-equated with the innate eternal sense of perfection.
451.00
Vector Equilibrium: Axes of Symmetry
and Points of Tangency in Closest Packing of Spheres
451.01 It is a characteristic
ofall the 25 great circles that each one of
them goes through two or more of the vector equilibrium's 12 vertexes. Four
of the great circles go through six vertexes; three of them go through four
ver-
texes; and 18 of them go through two vertexes.
451.02 We find that all the
sets of the great circles that can be generated
by all the axes of symmetry of the vector equilibrium go through the 12 ver-
texes, which coincidentally constitute the only points of tangency of closest-
packed, uniform-radius spheres. In omnidirectional closest packing, we
always have 12 balls around one. The volumetric centers of the 12 uniform-
radius balls closest packed around one nuclear ball are congruent with the 12
452.03
Great Circles of Vector Equilibrium 169
vertexes of the vector equilibrium of twice the radius
of the closest-packed
spheres.
451.03 The network of
vectorial lines most economically interconnecting
the volumetric centers of 12 spheres closest packed around one nuclear sphere
of the same radius describes not only the 24 external chords and 12 radii of
the vector equilibrium but further outward extensions of the system by closest
packing of additional uniform-radius spheres omnisurrounding the 12 spheres
already closest packed around one sphere and most economically intercon-
necting each sphere with its 12 closest-packed tangential neighbors, altogether
providing an isotropic vector matrix, i.e., an omnidirectional complex of vec-
torial lines all of the same length and all interconnected at identically
angled
convergences. Such an isotropic vector matrix is comprised internally entirely
of triangular-faced, congruent, equiedged, equiangled octahedraand telra-
hedra. This isotropic matrix constitues the omnidirectional grid.
451.04 The basic gridding
employed by nature is the most economical
agglomeration of the atoms of any one element. We find nature time and
again using this closest packing for most economical energy coordinations.
452.00
Vector Equilibrium: Great-Circle Railroad Tracks
of Energy
452.01 The 12 points of
tangency of unit-radius spheres in closest pack-
ing, such as is employed by any given chemical element, are important be-
cause energies traveling over the surface of spheres must follow the most eco-
nomical spherical surface routes, which are inherently great circle routes, and
in order to travel over a series of spheres, they could pass from one sphere to
another only at the 12 points of tangency of any one sphere with its closest-
packed neighboring uniform-radius sphere.
452.02 The vector
equilibrium's 25 great circles, all of which pass
through the 12 vertexes, represent the only "most economical lines"
of en-
ergy travel from one sphere to another. The 25 great circles constitute all the
possible "most economical railroad tracks" of energy travel from one
atom to
another of the same chemical elements. Energy can and does travel from
sphere to sphere of closest-packed sphere agglomerations only by following
the 25 surface great circles of the vector equilibrium, alwas accomplishing
the most economical travel distances through the only 12 points of closest-
packed tangency.
Fig. 450.11 A Axes of Rotation of Vector Eguilibrium:
A. Rotation of
vector equilibrium on axes through centers of opposite triangular faces
defines four equatorial great-circle planes.
B. Rotation of the vector equilibrium on axes through
centers of opposite square laces
defines three equatorial great-circle planes.
C. Rotation of vector equilibrium on axes through
opposite vertexes defines six equa-
torial great-circle planes.
D. Rotation of
the vector equilibrium defining twelve equatorial great-circle planes,
each of which passes through two opposite vertexes and two midpoints of the
edges of two opposite triangular faces. The axes of rotation pass through
opposite
square faces.
Fig. 450.11BProjection of 25 Great-Circle Planes in Vector Equilibrium System: The
complete vector equilibrium system of 25 great-circle planes,
shown as both a plane
faced-figure and as the complete sphere (3 + 4 +
6 + 12 = 25). The heavy lines show the
edges, of the original 14-faced vector equilibrium.
Fig. 457.30A Axes of Rotation of Icosahedron:
A. The rotation of the icosahedron on axes through
midpoints of opposite edges define 15 great-circle planes.
B. The rotation of the icosahedron on axes through opposite vertexes define six equatorial great-circle planes, none of which pass
through any vertexes. C. The rotation of the icosahedron on axes through the centers of
opposite faces define ten equatorial great-circle planes, which do
not pass through any vertexes.
Fig. 457.30B Projection of 31 Great-Circle Planes
in Icosahedron System; The com-
plete icosahedron system of 31 great-circle planes shown with the planar
icosahedron
as well as true circles on a sphere (6 + 10 +
15 = 31). The heavy lines show the edges of
the original 20-faced icosahedron.
Fie. 457.40 Definition of Spherical Polyhedral in 31 -Great-Circle Icosahedron System: The 31 great circles of the spherical icosahedron
provide spherical edges for three
other polyhedra in addition to the icosahedron itself, whose
edges are shown as heavy
lines. The shading indicates a typical face, as follows:
A. The rhombic
triacontrahedron with 30 spherical rhombic faces, each consisting of
four basic, least-common-denominalor triangle.
B. The octahedron with 15 basic,
least-conimon-denominalor spherical triangles.
C. The pentagonal dodecahedron with ten
basic. least-common-denominator spherical triangles.
458.04 Great Circles of Icosahedron 187
457.43 The spherical
pentagonal dodecahedron is composed of 12 spheri-
cal pentagons.
458.00 Icosahedron:
Great Circle Railroad Tracks of Energy
458.01Whereas each of the 25 great circles of the vector
equilibrium and
the icosahedron goes through the 12 vertexes at least twice; and whereas the
12 vertexes are the only points of intertangency of symmetric, unit-radius
spheres, one with the other, in closest packing of spheres; and inasmuch as
we find that energy charges always follow the convex surfaces of systems;
and inasmuch as the great circles represent the most economical, the shortest
distance between points on spheres; and inasmuch as we find that energy
always takes the most economical route; therefore, it is perfectly clear that
energy charges passing through an aggregate of closest-packed spheres, from
one to another, could and would employ only the 25 great circles as the great-
circle railroad tracks between the points of tangency of the spheres, ergo, be-
tween points in Universe. We can say, then, that the 25 great circles of
the
vector equilibrium represent all the possible railroad tracks of shortest
energy
travel through closest-packed spheres or atoms.
458.02 When the nucleus of
the vector equilibrium is collapsed, or con-
tracted, permitting the 12 vertexes to take the icosahedral conformation, the
12 points of contact of the system go out of register so that the 12 vertexes
that accommodate the 25 great circles of the icosahedron no longer constitute
the shortest routes of travel of the energy.
458.03 The icosahedron could
not occur with a nucleus. The icosahedron,
in fact, can only occur as a single shell of 12 vertexes remote from the vector
equilibrium's multi-unlimited-frequency, concentric-layer
growth. Though it
has the 25 great circles, the icosahedron no longer represents the travel of
energy from any sphere to any tangent sphere, but it provides the most eco-
nomical route between a chain of tangent icosahedra and a face-bonded icosa-
hedral structuring of a "giant octahedron's" three great circles, as
well as for
energies locked up on its surface to continue to make orbits of their own in
local travel around that single sphere's surface.
458.04 This unique behavior
may relate to the fact that the volume of the
icosuhedron in respect to the vector equilibrium with the rational value of 20
is 18.51 and to the fact that the mass of the electron is approximately one
over
18.51 in respect to the mass of the neutron. The icosahedron's shunting of
energy into local spherical orbiting, disconnecting it from the closest-packed
railroad tracks of energy travel from sphere to sphere, tends to identify
the icosahedron very uniquely with the electron's unique behavior in respect
to nuclei as operating in remote orbit shells
460.00
Jitterbug: Symmetrical Contraction
of Vector Equilibrium
460.01 Definition
460.011The "jitterbug" is the finitely closed, external vector
structuring
of a vector-equilibrium model constructed with 24 struts, each representing
the push-pull, action-and-reaction, local compression vectors, all of them
cohered tensionally to one another's ends by flexible joints that carry only
ten-
sion across themselves, so that the whole system of only-locally-effective
compression vectors is comprehensively cohered by omniembracing continu-
ous four closed hexagonal cycles' tension.
460.02 When the vector-equilibrium
"jitterbug" assembly of eight trian-
gles and six squares is opened, it may be hand-held in the omnisymmetry con-
formation of the vector equilibrium "idealized nothingness of absolute
mid-
dleness." If one of the vector equilibrium's triangles is held by both
hands in
the following manner-with that triangle horizontal and parallel to and above
a tabletop; with one of its apexes pointed away from the holder and the bal-
ance of the jitterbug system dangling symmetrically; with the opposite and
lowest triangle, opposite to the one held, just parallel to and contacting the
tabletop, with one of its apexes pointed toward the individual who is hand-
holding the jitterbug-and then the top triangle is deliberately lowered toward
the triangle resting on the table without allowing either the triangle on the
table or the triangle in the operator's hands to rotate (keeping hands clear of
the rest of the system), the whole vector equilibrium array will be seen to be
both rotating equatorially, parallel to the table but not rotating its
polar-axis
triangles, the top one of which the operating individual is hand-lowering,
while carefully avoiding any horizontal rotation of, the top triangle in
respect
to which its opposite triangle, resting frictionally on the table, is also
neither
rotating horizontally nor moving in any direction at all.
460.03 While the equatorial
rotating results from the top triangle's rota-
tionless lowering, it will also be seen that the whole
vector-equilibrium array
is contracting symmetrically, that is, all of its 12 symmetrically radiated
ver-
texes move synchronously and symmetrically toward the common volumetric-
center of the spherically chorded vector equilibrium. As it contracts compre-
hensively and always symmetrically, it goes through a series of geometrical-
transformation stages. It becomes first an icosahedron and then an octahedron
with all of its vertexes approaching one another symmetrically and without
twisting its axis.
460.04 At the octahedron
stage of omnisymmetrical contraction, all the
vectors (strut edges) are doubled together in tight parallel, with the vector
equilibrium's 24 struts now producing two 12-strut-edged octahedra congruent
with one another. If the top triangle of the composite octahedron (which is the
triangle hand-held from the start, which had never been rotated, but only
lowered with each of its three vertexes approaching exactly perpendicularly
toward the table) is now rotated 60 degrees and lowered further, the whole
structural system will transform swiftly into a tetrahedron with its original
24
edges now quadrupled together in the six-edge pattern of the tetrahedron, with
four tetrahedra now congruent with one another. Organic chemists would
describe it as a quadrivalent tetrahedral structure.
460.05 Finally, the model of
the tetrahedron turns itself inside out and os-
cillates between inside and outside phases. It does this as three of its four
tri-
angular faces hinge open around its base triangle like a flower bud's petals
opening and hinging beyond the horizontal plane closing the tetrahedron bud
below the base triangle.
460.06 As the tetrahedron is
opened again to the horizontal four-triangle
condition, the central top triangle may again be lifted, and the whole contrac-
tive sequence of events from vector equilibrium to tetrahedron is reversed; the
system expands after attaining the octahedral stage. When lifting of the top-
held, nonhorizontally rotated triangle has resulted in the whole system ex-
panding to the vector equilibrium, the equatorial rotational momentum will be
seen to carry the rotation beyond dead-center, and the system starts to
contract
itself again. If the operating individual accommodates this momentum trend
and again lowers the top triangle without rotating it horizontally, the
rotation
will reverse its original direction and the system will contract through its
previous stages but with a new mix of doubled-up struts. As the lowering and
raising of the top triangle is continuously in synchronization with the
rotating-
contracting-expanding, the rotation changes at the vector equilibrium's
"zero"-this occasions the name jitterbug. The vector equilibrium has
four
axial pairs of its eight triangular faces, and at each pair, there are
different
mixes of the same struts.
460.07 The jitterbug employs
only the external vectors of the vector equi-
librium and not its 12 internal radii. They were removed as a consequence of
observing the structural stability of 12 spheres closest packed around a
nuclear
sphere. When the nuclear sphere is removed or mildly contracted, the 12 balls
rearrange themselves (always retaining their symmetry) in the form of the
icosahedron. Removal of the radial vectors permitted contraction of the model-and
its own omnisymmetrical pulsation when the lowering and raising patterns are
swiftly repeated. It will be seen that the squares accommodate
the jitterbug contractions by transforming first into two equiangular triangles
and then disappearing altogether. The triangles do not change through the
transformation in size or angularity. The original eight triangles of the
vector
equilibrium are those of the octahedron stage, and they double together to
form the four faces of the tetrahedron.
460.08 In the jitterbug, we
have a sizeless, nuclear, omnidirectionally
pulsing model. The vector-equilibrium jitterbug is a conceptual system in-
dependent of size, ergo cosmically generalizable. (See Sees. 515.10 and
515.11.)
461.00
Recapitulation: Polyhedral Progression in Jitterbug
461.01 If the vector
equilibrium is constructed with circumferential vec-
tors only and joined with flexible connectors, it will contract symmetrically,
due to the instability of the square faces. This contraction is identical to
the
contraction of the concentric sphere packing when the nuclear sphere is re-
moved. The squares behave as any four balls will do in a plane. They would
like to rest and become a diamond, to get into two triangles. They took up
more room as a square, and closer packing calls for a diamond. The 12 ver-
texes of the vector equilibrium simply rotate and compact a little. The center
ball was keeping them from closer packing, so there is a little more compac-
tibility when the center ball goes out.
461.02 Icosahedron: The icosahedron occurs when the square faces are
no longer squares but have become diamonds. The diagonal of the square is
considerably longer than its edges. But as we rotate the ridge pole, the dia-
monds become the same length as the edge of the square (or, the same length
as the edge of the tetrahedron or the edge of the octahedron). It becomes the
octahedron when all 30 edges are the same length. There are no more squares.
We have a condition of omnitriangulation.
461.03 We discover that an
icosahedron is the first degree of contraction
of the vector equilibrium. We never catch the vector equilibrium in its true
existence in reality: it is always going one way or the other. When we go to
the icosahedron, we get to great realities. In the icosahedron, we get to a
very
prominent fiveness: around every vertex you can always count five.
461.04 The icosahedron
contracts to a radius less than the radii of the
vector equilibrium from which it derived. There is a sphere that is tangent to
the other 12 spheres at the center of an icosahedron, but that sphere is in-
herently smaller. Its radius is less than the spheres in tangency which
generate
the 12 vertexes of the vector equilibrium or icosahedron. Since it is no longer
Fig. 460.08 Symmetrical Contraction of Vector
Equilibrium: Jitterbug System: If the
vector equilibrium is constructed with circumferential vectors only and joined
with
flexible connectors, it will contract symmetrically due to the instability of
the square
faces. This contraction is identical to the contraction of the concentric
sphere packing
when its nuclear sphere is removed. This system of transformation has been
referred to
as the "jitterbug." Various phases are shown in both
left- and right-hand contraction:
A. Vector
equilibrium phase: the beginning of the transformation.
B. Icosahedron phase: When the short diagonal
dimension of the quadrilateral face is equal to the vector equilibrium edge length.
20 equilateral triangular faces are formed.
C. Further
contraction toward the octahedron phase.
D. Octahedron phase: Note the doubling of the edges.
****
194 System
461.04
the same-size sphere, it is not in the same frequency
or in the same energetic
dimensioning. The two structures are so intimate, but they do not have the
same amount of energy. For instance, in relation to the tetrahedron as unity,
the volume of the icosahedron is 18.51 in respect to the vector equilibrium's
volume of 20. The ratio is tantalizing because the mass of the electron in re-
spect to the mass of the neutron is one over 18.51. That there should be such
an important kind of seemingly irrational number provides a strong contrast to
all the other rational data of the tetrahedron as unity, the octahedron as
four,
the vector equilibrium as 20, and the rhombic dodecahedron as six: beautiful
whole rational numbers.
461.05 The icosahedron goes
out of rational tunability due to its radius
being too little to permit it having the same-size nuclear sphere, therefore
putting it in a different frequency system. So when we get into atoms, we are
dealing in each atom having its unique frequencies.
461.06 In the
symmetrical jitterbug contraction, the top triangle does not
rotate. Its vertex always points toward the mid-edge of the opposite triangle
directly below it. As the sequence progresses, the top triangle approaches the
lower as a result of the system's contraction. The equator of the system twists
and transforms, while the opposite triangles always approach each other rota-
tionlessly. They are the polar group.
461.07 Octahedron: When the
jitterbug progresses to the point where
the vector edges have doubled up, we arrive at the octahedron. At this stage,
the top triangle can be pumped up and down with the equatorial vectors being
rotated first one way and then the other. There is a momentum of spin that
throws a twist into the system-positive and negative. The right-hand octahe-
dron and the left-hand octahedron are not the same: if we were to color the
vectors to identify them, you would see that there are really two different
octahedra.
461.08 Tetrahedron: As thetop triangle still plunges toward the op-
posite triangle, the two comers, by inertia, simply fold up. It has become the
tetrahedron. In the octahedron stage, the vectors were doubled up, but now
they have all become fourfold, or quadrivalent. The eight tetrahedra of the
original vector equilibrium are now all composited as one. They could not es-
cape from each other. We started off with one energy action in the system,
but we have gone from a volume of 20 to a volume of one.* The finite clo-
* In vectorial geometry, you have to watch for the
times when things double up. The vectors
represent a mass and a velocity. Sometimes they double up so they represent
twice the value-or
four times the value-when they become congruent.
Fig. 461.08 Jitterbug System
Collapses into Tetrahedron: Polarization: The "jitter-
bug" system, after reaching the octahedron phase, may be collapsed and
folded into
the regular tetrahedron. Note that because the vector equilibrium has 24 edges
the
tetrahedra have accumulated four edges at each of their six normal edges. The
"jitter-
bug" can also be folded into a larger but incomplete tetrahedron. Note that in this case
the two sets of double edges which suggest polarization. |