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Sandpile Chalice

Here we revisit the idea depicted in Elliptical Spotlights. By filling in the space between the spotlights, we obtain a continuous surface known as the sandpile surface over an ellipse. The surface is singular, with four swallow-tails joined by four cusp edges and two lines of self-intersection. The four swallow-tails form the corners of a tetrahedron, with the cusps and double-curves forming the edges.

The self-intersection is hard to see in Elliptical Spotlights, but is more apparent here. The sandpile surface is a ruled surface, and we continue to use color here to indicate the rulings and which part of the ellipse they come from. In the video, Fronts and Centers, this surface is rendered in a metalic silver, forming an object that appears to be a silver chalice, which gives this image its name.

Like Elliptical Spotlights and Ellipse Evolute, this image appeared in Beyond the Third Dimension, and as part of the video, Fronts and Centers.

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Created: 13 Oct 2003
Last modified: Oct 13, 2003 10:40:53 PM
Comments to: dpvc@union.edu
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