The Triangles Which Aren't There

George W. Hart

This is a 12-inch diameter one-of-a-kind sculpture assembled from sixty identical pieces of laser-cut acrylic plastic (Plexiglas). The long title, The Triangles Which Aren't There, refers to an interesting visual effect it creates. It is very difficult to perceive the structure from a photograph, but in person you at first see it as a set of bars which form twenty interlocked triangles. Each triangle links with three others. The following image highlights two of them, indicating how they are linked but do not directly touch:


Because they do not touch, the twenty triangles would fall into a loose jumble if weren't for other small parts which hold everything together. But more importantly, these small parts hint at twenty additional larger triangles, which aren't completely there. One of these outlined triangles lies behind each of the complete triangles, but is rotated relative to it. The two corresponding incomplete triangles are highlighted in the following image:

The sculpture is designed to hang. As it slowly rotates, the eye all-of-a-sudden connects the parts of the incomplete triangles and perceives them as complete entities. Geometrically, all the triangles are derived by truncating the uniform compound of ten tetrahedra. One set of five tetrahedra is truncated to a slightly deeper depth than the other five. Interestingly, everything is accomplished with sixty copies of a single shape of part. The part is a long bar that makes up one side of one of the triangles which is there, overlayed with two short bars which make up parts of two of the triangles which are not there. Here are the parts as I receive them from the laser-cutter and am in the process of peeling off the protective paper:

The structure may or may not become clearer by studying this computer-generated image that I produced when designing the sculpture:

Here is the template, if you want to try to make your own copy.

Copyright 2003, George W. Hart