The "regular solids" are important in many aspects of chemistry, crystallography, and mineralogy. Keep in mind that each field tends to use slightly different nomenclature for the same thing, and each can have different uses for the same name. For example, an "octahedron" is a regular eight-sided solid, but it also describes the coordination geometry, octahedral, of many compounds (imagine an atom at the center of an octahedron and six other atoms, one at each corner). Be patient while the applets load. Drag your mouse over the figures to rotate them.
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The basic cube is certainly one of the most important of the regular solids. By rotating the cube you can see four-fold axes (one in each face), three-fold axes (one down each corner) and two-fold axes (along each edge).
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The tetrahedron also possesses each of the axes in the cube. In addition to the basic tetrahedron shown on the left, an example of tetrahedral coordination is shown on the right.
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The octahedron is shown on the left and octahedral coordination on the right.
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The dodeahedron is of importance primarily in discussing the morphology of crystals. To see how the dodecahedron form and other forms combine to give different morphologies, look at the " Isometric Crystal System" page of the IUMSC server.
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Of course we have to have the buckyball.
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For the solid figures above, you can convert to and from a wire-frame figure by typing "w" when the cursor is over the figure.
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Indiana University Molecular Structure Center
