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These projections would correspond to the network of lines seen in looking through a glass paperweight of the given shape, the lines being formed by the joining of the several faces. The dodecahedron and icosahedron, having more faces, yield more intricate patterns, and there is no limit to the variety of interesting designs obtainable by these direct and simple means.
That the universe should have assumed the form of a wreath is certainly a matter for astonishment; but it would have been still more astonishing if it had been a cube, a rhomboid, or a dodecahedron, for then we should have had to suppose that something resembling the forces that shape crystals had acted upon the stars, and the difficulty of explaining the universe by the laws of gravitation would have been increased.
Spangles and specks are found; but the greater part of the dust is granular, increasing to 'shotty gold. The natives divide the noble ore into 'dust-gold' and 'mountain-gold. The latter would consist of nuggets, 'lobs, or pépites, and of crystals varying in size from a pin's head to a pea. The form is a cube modified to an octahedron and a rhombic dodecahedron.
The fourth regular solid, or cube, is formed by the combination of four isosceles triangles into one square and of six squares into a cube. The fifth regular solid, or dodecahedron, cannot be formed by a combination of either of these triangles, but each of its faces may be regarded as composed of thirty triangles of another kind.
Place: the temporal mood of the Oversoul, playing through that particular facet of the dodecahedron, which is Greece. The combinations and interplay of these two, plus the energies for good or evil of the souls there incarnate, give as their resultant the whole life of the race.
You know Plato's idea that the world is a dodecahedron or twelve-sided figure. Now in Plato's day, much that every schoolboy knows now, was esoteric known only to the initiated. So I think Plato would have known well enough that this physical earth is round; and that what he meant when he spoke of the dodecahedron, was something else.
His theory was this: "Around the orbit of the earth describe a dodecahedron the circle comprising it will be that of Mars; around Mars describe a tetrahedron the circle comprising it will be that of Jupiter; around Jupiter describe a cube the circle comprising it will be that of Saturn; now within the earth's orbit inscribe an icosahedron the inscribed circle will be that of Venus; in the orbit of Venus inscribe an octahedron the circle inscribed will be that of Mercury."
Other sages adhered to the mathematical system of squares and triangles; the cube, the pyramid, and the sphere; the tetrahedron, the octahedron, the icosahedron, and the dodecahedron.
He sprang upright then awake, sure: they were diamonds, those bits of glass, big celestial ones, not of earth, in hundreds; when he passed his hand along the meteorite he felt it leprous, octahedron, dodecahedron, large and small: if they were truly diamonds, he divined that their owner must be as wealthy as some nations.
Is their opinion true who think that he ascribed a dodecahedron to the globe, when he says that God made use of it in delineating the universe? For upon account of the multitude of its bases and the obtuseness of its angles, avoiding all rectitude, it is flexible, and by circumtension, like globes made of twelve skins, it becomes circular and comprehensive.
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