icosahedron in A Sentence

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    The 20-sided shape of the Magic 8-Ball die is an Icosahedron.

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    However, one positive outcome of building the enneacontahedron was that it showed that five octahedra could be connected to an Icosahedron so that it would put neighboring icosahedra at the vertices of a regular pentagon.

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    Returning to the picture above, if you're familiar with the regular octahedron and Icosahedron, it's not too hard to see that the 30-unit construction is an elevated Icosahedron and the 12-unit construction is an elevated octahedron.

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    Well, anything worth doing once is worth doing twice, so I removed one face each from another Icosahedron and from the structure so far, and then was able to link the two together, creating a sort of barbell.

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    5

    This correspondence holds because the twenty triangular faces of the Zometool hub are at exactly the same angles as the faces of an Icosahedron(in fact, the zometool hub is simply a cantellated Icosahedron), and because the yellow Zometool strut has the same 60-degree rotation between its oppposite ends as the octahedron does between its opposite faces(arising from the fact that the regular octahedron is also the triangular antiprism).

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