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The Alpha particle is the nucleus of the element
helium, as well as a form of radiation. It is
comprised of two protons and two neutrons and is a
very stable particle. So too are other atomic nuclei
which can be considered agglomerations of multiple
Alpha particles. It's possible this stability is related
in part to the fact that four spherical volumes are
most efficiently packaged in a tetrahedronal array.
This is significant since a tetrahedron is not only a
complete structural form, but also because it is
geometry's minimum requirement for a three
dimensional form. And most importantly, it is the
most stable of all geometric arrangements.

As atomic nuclei, protons and neutrons collectively are called "nucleons". Modeling their masses as
spherical volumes produces a corresponding average mass-volume for a nucleon of 1837.418162. . . with
respect to the electron's mass-volume of 1 unit.* The radius of a sphere so scaled is 7.5981255. . . This creates
an edge-length on the Alpha particle's internal structural tetrahedron measuring 15.196251. . . Close
scrutiny shows that this tetrahedron's proportions are patterned on fundamental geometric ideals based in
unity and rooted in the very heart of geometry.

The tetrahedron to the left is the Alpha
particle's internal structural tetrahedron. It is, to
a .9998 degree of congruence, patterned on the
natural distribution of One Surface Unit. This
tetrahedron is, in essence, the manifestation of
that "ideal" form magnified in length by the
power of 10, making its' surface 100 times, and
its' volume 1000 times its' patterned "ideal".

Geometry's minimum expression of a surface unit is in the form of an equilateral triangle. This is
because three points is the minimum requisite for enclosing an area. The triangle is equilateral because the
points are most economically closest packed. In order to put this form to some kind of natural scale, to give it a
specific size, this triangle can be spun around it's planar center forming a circle of greater area in the
process. The now two areas can be compared and units defining each assigned. If the circle of area be
considered One Surface Unit, then the area of the equilateral triangle is: 0.4135. . . . Likewise, if
the three dimensional tetrahedron (geometry's minimum volumetric form defined by four points) is spun into
the form of a cone, and this cone be quantified as One Volumetric Unit, then the tetrahedron's volume, like the
spun triangle, is:

0.4135. . . .

This ratio, 1/0.4135. . . . is built into the geometry of these forms and holds true regardless of their
size. Moreover, an area of 0.4135. . . . And a volume of 0.4135. . . . are special quantities favored by the
geometry of form.