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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.
To the earth then, which is the most stable of bodies and the most easily modelled of them, may be assigned the form of a cube; and the remaining forms to the other elements, to fire the pyramid, to air the octahedron, and to water the icosahedron, according to their degrees of lightness or heaviness or power, or want of power, of penetration.
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.
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.
Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury."
Secondly, by a great bird made of wood, the wings of which should be kept in motion. Thirdly, by rockets, which, going off successively, would drive up the balloon by the force of projection. Fourthly, by an octahedron of glass, heated by the sun, and of which the lower part should be allowed to penetrate the dense cold air, which, pressing up against the rarefied hot air, would raise the balloon.
After the cube, the octahedron, and the various forms of pyramid and prism have been mastered, may come the more complex regular bodies the dodecahedron and icosahedron to construct which out of single pieces of cardboard, requires considerable ingenuity.
Then for the first time did we hoist the cable-ship insignia on the foremast head, three balls, which at a little distance looked not unlike the sign of a pawnshop, though our three balls were hung vertically from the masthead, two red ones with a white octahedron shape between them.
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."
This regular solid of four-dimensional space consists of sixteen cells, each a regular tetrahedron, thirty-two triangular faces, twenty-four edges and eight vertices. It is the correlative of the octahedron of three-dimensional space. First it is necessary to establish our four axes, all mutually at right angles.
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