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Updated: May 19, 2025
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.
It was exactly twelve years since he had been born, a tiny, shapeless, senseless, helpless, toothless, speechless, useless, feeble, deaf, myopic creature; and now he was a school-boy, strong, healthy, big, and clever, who could define a dodecahedron and rattle off the rivers of Europe like a house on fire.
Pythagoras, that the world was formed of five solid figures which are called mathematical; the earth was produced by the cube, the fire by the pyramid, the air by the octahedron, the water by the icosahedron, and the globe of the universe by the dodecahedron. In all these Plato hath the same sentiments with Pythagoras.
Now I have to remind you of certain conclusions worked out in an article 'Cyclic Law in History, which appeared some time back in The Theosophical Path: that there are, for example, three great centers of historical activity in the Old World: China and her surroundings; West Asia and Egypt; Europe. Perhaps these are major facets of the dodecahedron.
"The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn.
On the strength of this conceit, he supposed that the distances of the planets were regulated by the sizes of the five regular solids described within one another. "The Earth is the circle, the measurer of all. Round it describe a dodecahedron; the circle including this will be Mars. Round Mars describe a tetrahedron; the circle including this will be Jupiter.
"Here are a dozen specimens which may interest you the octahedron, the rhombic dodecahedron, the triakisoctahedron and the hexakisoctahedron." He spread them along the table with a sweeping gesture of his hand, colorless, inert pebbles, ranging in size from a pea to a peanut. "And now, you ask, where do they come from?" The others nodded unanimously.
Very recently a paper was read before the Mathematical Society of London by Mrs. Bryant, Sc.D., on the geometrical form of perfectly regular cell structure, illustrated by models of cube and rhombic dodecahedron. In another section, Mme. Traube Mengarini studies the function of the brain in fishes; while, in our own country, Mrs. Commonplace! Why, what is commonplace?
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