May not one evidence of this be an easier recognition of the Theosophic Light that has been passed from hand to hand down the ages? Many have been its disguises, many and strange the lamps holding it, often obscured it has been, again nameless—but ever the one Light, the one Flame, shining upon and enlightening all men.
THE PYTHAGOREAN SOLIDS:
by F. J. Dick, M. Inst. C. E., M. Inst. C. E. I.
Students of The Secret Doctrine and of ancient teachings such as those of Pythagoras, the Kabala, and the sacred books of different races and epochs, are often puzzled by the frequent references to Number, and to elementary plane forms like the circle, triangle, and square. It may be surmised that these symbols refer to meta-physical forces of various orders concealed within the "atom" and within nature generally. For nature is built, obviously enough, upon some internal principles of structural harmony. Without discussing the many avenues of thought suggested by a study of the five regular solids, the main features of these forms may be briefly summarized.
In the first place, they may be all considered as generated by Twelve Points on the surface of the Sphere, at equal adjacent distances, or by six diameters of the sphere mutually inclined at angles whose tangent is 2, the number of the octave in music. Joining each of the twelve with every other point, we have 66 lines, of which 36 are internal. Six of the latter being diameters, there remain 30, intersecting at 20 points, which give the 30 edges of the internal dodecahedron. The 30 outer, or external lines of the 66, form the edges of the icosahedron.
Joining one set of alternate corners of the Dodecahedron by 12 lines, a cube appears. So far, there are 33 points defined, including the center of the sphere. Joining opposite corners on each Cube-face by 12 lines, two interlaced tetrahedrons appear. These define, by their intersection, 6 new points and 12 new lines forming the Octahedron, beautifully poised in the heart of the Sphere.
Thus only 39 points, including the central point, are needed to define the Pythagorean solids, only one solid form being repeated, the Tetrahedron, which in fact is seen to repeat itself ten times. For between the interlaced Tetrahedron corners and the eight faces of the included Octahedron, eight smaller Tetrahedrons are seen.
The interlaced Tetrahedrons suggest the origin of the plane symbol—the interlaced triangles; but the full beauty of the symbol does not appear until we notice that the axis of symmetry of the Tetrahedrons coincides with the diagonal of the Cube, and that the orthographic projection of all these on a plane perpendicular to the diagonal gives a perfect hexagon with the interlaced triangles in the center. The interlaced Tetrahedrons—one a reflection of the other—in fact define the eight corners of the Cube. The Tetrahedron is "3," and the Cube is "4" (or 6). So we see one way in which the "three fall into the four," and why it is a septenary, and a decad, as well as a three, or a four, according to the various aspects and interrelations considered of the electric, rotary, magnetic, or vibratory forces symbolized by the various lines.
Science has already reached the speculation that the hypothetical carbon "atom" has a tetrahedronal form. Let us look at this Tetrahedron with the eye opposite the middle of an edge and in line with the center. The two opposite edges now form the Cross, composed of two equal lines, but separated by a space. One is reminded of an electric wire, and a magnetized needle placing itself at right angles to, although at some distance from, the current in the wire. Thus the opposite edges, whether as rotational vectors or in some other way, indicate a connexion with the dual forces of attraction and repulsion. The Tetrahedron, a triangular pyramid, may be a Fire-symbol. In any case the following passage is suggestive: