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[Art from B3D]


Artwork from "Beyond the Third Dimension"

These diagrams are from Thomas Banchoff's volume in the Scientific American Science Library series, Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions, (W. H. Freeman and Co., New York, 1990). While a graduate student at Brown University, I produced most of the line art for this book (more than 200 images in all) using the 2D drawing program Aldus Freehand (now Macromedia Freehand). This was the first time Freeman had used computer-generated artwork, and they were surprized at how quickly we could produce updates and corrections to the diagrams.

In this selection of images from three chapters of the book, we see the following: at the upper left, an unfolded hyperpyramid having a cubical base with apex directly over (in four-space) one of the corners of the base cube; at the upper right, an unfolded and exploded hypercube; at lower left, an image of the {\it stella octangula}, the stellation of an octahedron that fits within a cubical box; at the center, purple pyramids illustrating how the volume of a pyramid does not depend on the position of the apex (since the slabs are all the same volume in either case); and finally, at the lower right, a pyramid indicating how the volume of a triangle-based pyramid (e.g. a tetrahedron) is half the volume of the corresponding square-based one.

The production of the artwork for this book is the subject of the article "Illustrating Beyond the Third Dimension" that appears in my publications list.

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Created: 08 Sep 2001
Last modified: Jan 6, 2002 11:20:23 PM
Comments to: dpvc@union.edu
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