Bridges: Mathematical Connections in Art, Music, and Science (2002)

Pages 151–156

I exhibited 3-dimensional designs made from Rubik's cubes at the Bridges Conference two years ago. I left the conference with new ideas brought forth by the conference participants. Ken Landry [1] suggested a block model for a design that I named after him, the Landry Staircase (figure 3). This design ushered in a new type of non-cubical designs, the so-called block designs. Craig Kaplan [2] gave me an idea for a simple but rather nice cubical design. A call for a "practical application" of those designs prompted a response: use the designs as chandeliers, placing small candles at strategic points on the design, creating various arrays of lights. In complete darkness those lights form a specific configuration "suspended in air." I am assuming that it is so dark the designs cannot be seen; only the lights penetrate the darkness. Two years have passed since the conference and I still cannot find anyone, on or off the web, who creates those designs. People at the conference complained about the "complexity" of the design problem and its solution and suggested that a computer be used to implement those designs. But how to do it? I am not a computer programmer. I solved the problem purely analytically. All you need to do is use existing mathematics and develop some rules to simplify the solution and implement those designs. After reviewing a few basic concepts, I will show you how to construct Vasarely, my oldest non-cubical design. I encourage you to go through the process of twiddling all 102 Rubik's cubes. After that, I will discuss other non-cubical designs. By all means, build the Landry Staircase if you can get the required 216 Rubik's cubes.

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