Sacred Geometry and Symbolic Polyhedra

The symbolic mechanism can be applied through the use of three-dimensional solids. The sphere is a perfect three-dimensional equivalent of the circle, just as the cube is of the square and the tetrahedron of the triangle. The other regular or semi-regular polyhedra that can be inscribed in a sphere all result from the union of Sacred Numbers that make them suitable for expressing, through symbolic relationship, special metaphysical realities. The Ternary $3$ and the Quaternary $4$ unite in the octahedron, the Number $5$ and $12$ give life to the dodecahedron, etc.

From a practical point of view, these must be transparent, having on their faces the Names of Power appropriate to the spiritual entity and the metaphysical reality they represent. Finally, they must be illuminated from within and therefore be luminous sources because, passing through the Names of force written on the faces of the solid, the light is colored and acquires the corresponding spiritual characteristic.

The Sphere

The Sphere is the most symmetrical solid, equal to itself under the action of any rotation, it has continuous, indefinite symmetry. Since it has neither beginning nor end, it is a symbol of Eternity. The Sphere, as a portion of fluid space circumscribed, closed and limited, refers to creation and the cosmos beyond which lies the metacosmos and the uncreated world.

It is also a symbol of perfection, of the Cosmos and of Man. In the individual domain, the spherical Man identifies the perfection of origins and the epilogue of Man who has passed through the stages represented by all regular polyhedra: tetrahedron, octahedron, icosahedron, cube and dodecahedron.

The Sphere is also associated with the symbol of the pearl, the Kingdom of Heaven, a Sophianic, lunar, mystical symbol, linked to water and Woman, and which is the science of the heart.

Tetrahedral Symmetries

The most important uniform polyhedra with tetrahedral symmetry are the Tetrahedron and its Archimedean derivative, the Truncated Tetrahedron. As always happens in the case of polyhedra having the same symmetry, the meaning of the two solids is similar, with the truncated tetrahedron being only a variation and specification of the tetrahedral figure.

For solids with tetrahedral symmetry, Number $3$ is particularly important and secondarily Number $4$, especially in its meaning of $1 + 3 = 4$; that is, of the hidden and invisible Unity of the Ternary, its manifestation. Parallel to this, on the geometric front, their symbolism is linked to that of the Triangle of which they are the three-dimensional equivalent.

From Number $3$ derive Numbers $6$, $12$ and $24$ also associated with these solids. Tetrahedral symmetry possesses in fact $24$ elements, of which $12$ are rotations.

The Tetrahedron

The regular Tetrahedron is a symbol of "fire" and has the letters of the sacred Name on its faces, since it takes the character of "Divine Fire", therefore it represents the sanctuary of the Divinity itself and the name "Zabulon" which means "heaven, the dwelling of God".

The Tetrahedron achieves perfect balance between $4$ points or vertices equidistant in space. In this sense it is the perfect three-dimensional equivalent of the equilateral triangle. In the cosmogonic field it corresponds to the element fire. Although formed only by triangles, it contains the numerical element Four $4$ and for this reason refers to hidden fire, to the dark fire of the Saturn epoch and also to the fire of vitriol in the depths of the Earth.

It is the animating fire of matter, the primordial element from which all elements derive. The fire element also corresponds to the deepest state of consciousness, comparable to that of trance, which, with continuity of consciousness, the initiate must traverse while maintaining the connection with the presence of Christ.

If it bears the Name of four letters יהוה (YHVH), the Tetrahedron symbolizes the "Divine Fire", the Presence of God in a concentrated form. Fire was the first symbol revealed to Man in remote epochs to identify the Divinity.

The tetrahedral Man is therefore one who, having purified the principles - spirit, soul and body - through ascesis and catharsis, has found himself worthy of receiving Grace in the form of celestial fire. The image of the tetrahedron represents the three "fires" of human consciousness that merge with Divine Fire in a single flame.

The Numbers that characterize the Tetrahedron are Three $3$, Four $4$ and, secondarily, Six $6$. The Three $3$ by way of the triangular faces, the Four $4$ that identifies the number of vertices and faces of the solid and the Six $6$ for the number of edges. Finally, if we consider the synthesis number of the Tetrahedron, being the polyhedron formed by four triangular faces, we find the number $12$ which coincides with the number of rotation axes of the solid.

The previous Numbers harmonize around the figure of the Tetrahedron with $3$ being the symbol of Fire, while $4$ or the Quaternary indicates its manifestation. The $6$ is the symbol of the Human-Divine alliance realized with the descent of Fire and finally the $12$ is the regal symbol of complete manifestation and revelation.

Truncated Tetrahedron

The Truncated Tetrahedron is an Archimedean polyhedron obtained in the passage from Tetrahedron to Octahedron through the duality operation. The Tetrahedron is indeed a self-dual figure, that is, it is the dual of itself, but in the passage from Tetrahedron to Tetrahedron, from "Fire" to "Fire" there is a middle point, a place of bifurcation, identified by the Octahedron, symbol of the "Air" element. It is thus possible to say that the "Air" element derives by separation from the "Fire" element.

The Truncated Tetrahedron unites in a single vertex two regular hexagons, reconciled by a triangle.