For example, as the equilateral triangular area, it is the
amount of surface difference that geometry must account for when
two One Surface Unit spheres fuse volumes into a single sphere. And
if this triangular area be folded into the surface of a tetrahedron,
then two of these tetrahedronal volumes account for the excess
volume if one of the One Surface Unit spheres divides it's surface into
two new equal sized spheres. Evidence that geometry especially likes
accounting with this packaging scheme is the fact that this
tetrahedron with a surface equal to 0.4135.. . . . has the three
vertexes of it's base triangle commensurate to the One Surface Unit
sphere's circumference, while it's height measure is the diameter of
each of the two 1/2 surface unit spheres (making for the
arrangement to the right).

Tetrahedron accounting for surface and volume differences

In the case of the 0.4135.. . . .unit volume tetrahedron,
each triangular face = 1.000 surface unit. And when this
tetrahedron spins into a cone, its' volume = 1.000.. And
the height of this cone (and tetrahedron) is the diameter of a
sphere having volume = 1.000.. Now when this tetra-volume is
divided into eight equal portions (all tetra-forms) each of these
tetrahedron's surfaces = 1.000. unit. Arrange the eight tets so
that each shares a common vertex forming a vector equilibrium
(the formal structure defining the closest packing of spheres)*
and the largest sphere that can be held within it's confines has a
volume = 1.000. The smallest sphere that can embrace the
vector equilibrium has a volume of 1.837. . . (patterning the
mass-volume of the average nucleon).

Vector Equilibrium

So, in the geometry of four 1837-unit- volume spheres, in their most efficient packaging form, we can see a
parallel tetrahedronal structure having a volume of 413.5. . . . and creating triangular faces of 100 areal
units, and a 1000 unit "spun into Cone" volume.

Clearly the Alpha particle's structural
tetrahedron is patterned on these formative
fundamental geometric relationships which
themselves are ultimately based on second and
third "powerings" of the same One Unit. But even
the first power expression of The Unit, a line one
unit in length, shows geometry's "built in" bias for
mass-volume relationships on the order of the
electron and nucleon. For a single line One Unit in
length, in the form of the edges of a regular
tetrahedron, creates a volume of 1/1833. And
proof that geometry likes this fundamental unit of
length manifesting as a tetrahedron is the fact that
exactly three of them stacked atop one another
equal the height and edge-length of One Surface
Unit in the form of a cube. In fact, this same cube's
sub-structuring shows it to be comprised of 125 sub-
cubes with each having a volume of 1/1837, which is
the mass of the electron compared to the average
nucleon mass of 1.000..

* Equal-radius-spheres closest packed together form an internal matrix consisting of tetrahedrons and
octahedrons. Each sphere has an omni-surround of twelve other spheres. However, the maximum possible
density occurs only in the tetrahedronal components of the structure.

"One Unit" in the forms of a tetrahedron's edges and the surface of a cube

2.