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Updated: May 14, 2025
From the triangle of which the hypotenuse is twice the lesser side the three first regular solids are formed first, the equilateral pyramid or tetrahedron; secondly, the octahedron; thirdly, the icosahedron; and from the isosceles triangle is formed the cube. Let us now assign the geometrical forms to their respective elements.
Now, a year or so ago, I had occupied my leisure in taking a London science degree, so that I have a smattering of physics and mineralogy. The thing was not unlike an uncut diamond of the darker sort, though far too large, being almost as big as the top of my thumb. I took it, and saw it had the form of a regular octahedron, with the curved faces peculiar to the most precious of minerals.
"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.
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