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Archimedian Solids

© Copyright 2003, Jim Loy

We know that there are only five Regular Solids. These are polyhedra, three-dimensional figures with identical regular polygons for faces, in which all of the vertices are the same (same number of intersecting polygons). What if we build polyhedra out of two or more regular polygons, each with the same length edge, and with the polygons distributed regularly (the same at each vertex, the whole object having a spherical symmetry)? Above left, we see one of these, called a cuboctahedron, being halfway between a cube and an octahedron (take a cube and cut off all the corners, or take an octahedron and cut off all the corners). Another (the truncated tetrahedron) is shown above right. It turns out that there are thirteen of these Archimedian solids. These are also sometimes called semiregular polyhedra. See MathWorld - Archimedean Solid.

Each of these polyhedra has a dual (see Regular Solids), and these are still more complicated objects.

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