Ninety binder clips (with 60 missing handles) arranged in a ball made with hexagons and stars.

Designed and constructed in April, 2011.

[Zodiac: inside view]

A view from inside the Zodiac.

Many binder clips are interlocked into an airy ball composed of 20 hexagons and 12 stars. There are 90 clips but only 120 handles: each clip in the middle of a star is missing one handle. If these were put back in, the polyhedral structure would correspond to a "rectified truncated icosahedron," obtained by replacing each vertex of a "soccer ball" polyhedron (a.k.a. truncated icosahedron) with a triangle. This rectification process is discussed more at the related sculpture, Clipped Corners, which uses a similar vertex-connection mechanism. This "rectified soccer ball" polyhedron cannot be built with all faces regular, so it is not one of the Archimedian solids.

[Rectified soccer ball]

Cutting off the corners of a "soccer ball", a.k.a. truncated icosahedron (left) produces a "rectified truncated icosahedron" (right), which cannot be built with perfectly regular faces. In this image, the triangles are not exactly equilateral.

In his work Timaeus, Plato describes a very precise theory for how the universe and its elements are constructed from the five regular polyhedra, which are thus known as Platonic solids. For example, since the cube is the sturdiest and easiest to construct of the five polyhedra, Plato assigns this to "earth." Similar discussions lead him to correlate "fire" with the tetrahedron, "water" with the icosahedron, and "air" with the octahedron. As there are four elements and five Platonic solids, one is necessarily left out. Here is Plato's explanation:

And there is a fifth figure (which is made out of twelve pentagons), the dodecahedron—this God used as a model for the twelvefold division of the Zodiac. (Plato's Timaeus, translated by B. Jowett, Project Gutenberg, 2008)
While this may be an overzealous translation—an alternative by the same translator reads, "There was yet a fifth combination which God used in the delineation of the universe." (Elpinor, 2006)—the correlation of the twelve faces of a dodecahedron with the twelve constellations of the Zodiac seems universally understood. My Zodiac highlights this relationship: there is one star (constellation) located at each of the twelve faces of a dodecahedron.

Copyright © 2011–2020 by Zachary Abel. All rights reserved. Last updated on 4/7/2020.