

Tetrahedron and Tetrahedral Sphere 
The TETRAHEDRON is one of the
platonic bodies. It has four corners and four
regular triangles as sides.
There are three pairs of othogonal
edges, the total number of edges is six.
The TETRAHEDRAL SPHERE is the central projection of the tetrahedron onto the surface of the unit sphere. The triangular sides of the tetrahedron become spherical triangles on the surface of the sphere. 
Tetrahedral Sphere and the PSE 
The four electrons sit at the corners of a tetrahedron. Alternatively, if the electronic charges are assumed to be spread out evenly  in this highly symmetric static model  each electron covers one of the four spherical triangles on the surface of the sphere. The element with Z=4 electrons is the element Beryllium. 
Four electrons in space and the topical quantum number 
Two electrons define a line, three a plane. This plane
may have any orientation in space. Therefore, to define
threedimensional isotropic space, four electrons are required.
Since under the supposition that the nucleus, consisting of
different kinds of particles, does not contribute to the
definition of threedimensional isotropic space, in case of
the atomic shell electrons also at least four electrons are required
for granting highest symmetry.
In the state of highest symmetry, the electrons are arranged to form a
tetrahedron. Each two of the four electrons at
the corners of the tetrahedron may be viewed as
having opposite spin and sitting on one of two
orthogonal edges. Thus, in addition to the spin
quantum number s, for full classification,
a new quantum number, which shall be called the
topical quantum number c , is required.
A visualization of a pair of electron pairs with
orthogonal 
Rotation  To rotate the spheres, click on a selected sphere and drag the mouse. 
See also 

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