![]() Though it is impossible, you can create a version of it in real space, made so you can look at it from one angle and it will look real. This was originally drawn in 1934 by Swedish artist Oscar Reutersvärd and later made popular by Lionel and Roger Penrose. Here is the basic impossible figure it is based on. The good news was that we picked up a nice drafting table for me, cheap. But it was a time of downsizing for Lockheed and soon they were laid off. The draftsmen at Lockheed, where my dad worked at the time, were quite impressed and put it up on their walls. And then I shaded it the best I could, given it is, after all, impossible. I used a drafting set to make the basic shapes. And the felt pen I used wasn't exactly the best tool to use. It was drawn with a Flair pen on the harshest Olivetti copy paper, so it has colored a bit through time. I drew it only a couple of months after my grandfather died, so it was clear that my obsession with impossible figures might have come from my need to process the situation. I drew the Triangular Symbol in summer 1969 when I was but 13 years old. But I created one in 1969 based on the impossible triangle. I have written about impossible figures before. John Derry and I spent many, many hours searching for the right icons for brushes, for features of brushes, for effects, for tools, for everything. They are both interesting pastimes and also they can be real work, as we will see. Imagination and simple tinkering can lead to the impossible figure. This is done by imagination and also by requirement. I never showed its other side, and so that remains a mystery.Īt some point, though, three-dimensional figures need to be transcended. What is this trying to be? I imagine it is a folded bit of paper, arranged in a triangle. On the same sheet I found another drawing. Perhaps this is a button from an old corduroy jacket. I can't even say what all the objects are, but I did find them interesting to imagine at one point. There are plenty of shapes that I have drawn over the years, most of them are found on the backs of meeting notes or on Excel spreadsheet printouts. And it's also obvious, since the vertex of the rhombic dodecahedron is actually at the center of a neighboring cube. Rhombic dodecahedra can fit together and tile space perfectly like cubes, which I find interesting. Constructing one with pencil and paper is easy, since the height of each pyramid is exactly one-half a cube edge length. Imagine a cube with short pyramids on each face. I show a rhombic dodecahedron superscribing a cube. This shape is the basis of a garnet crystal. It isn't well-known, but the dodecahedrons - both the platonic one and the rhombic one - can superscribe a cube. I like, for instance, to imagine how objects intersect, or how other objects can be contained inside them. I can almost feel the edges around the missing corner. I like the idea of something having a real three-dimensional heft to it. So I reorient the object in my mind to draw it. Otherwise I probably can't tell what it is. For a snub cube, I show the snub facing the viewer. And then I draw.Īnd when I draw, I try to find the proper orientation to depict the object and show its own characteristic features in the best light.įor a cube, I almost never draw it in such a way that I can't see its inherent dimensionality. ![]() I imagine holding them in my hand, reorienting them, looking at them. I know I am constantly drawing forms and shapes, trying to figure them out or reason about their volume. Ironically, it is two-dimensional pen and paper that becomes the practice field for three-dimensional cognition. And it is a salve for the rougher times of our lives. So I constantly draw pictures, drawing on my creativity to help me visualize. ![]() Using our own hand to sketch out an idea is a natural step for our creativity. As the voice is our one built-in instrument for our hearing, so is hand-drawing the main expression for vision. And there is nothing more visual than drawing.
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