Special Topics:Tilings

In 1887, Lord Kelvin posed the problem of finding the partition of space into equal volume cells minimizing the interface area. He suggested a partition which is basically the Voronoi cell for a BCC lattice. Robert Phelan and Denis Weaire of Trinity College, Dublin, have found a structure using two types of cells that has 0.3% less area than Kelvin's. This picture shows 9 opaque cells.

How to make it: The Surface Evolver, a program written by Ken Brakke with support from The Geometry Center, was used to compute the areas involved. Geomview was used to set up the appearance and point of view, and RenderMan was used to create the final image.

Image created: February, 1994

Copyright © February, 1994 by The Geometry Center, University of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 6k gif), medium (500x447 65k gif), or original size (1800x1608 1,870k tiff).

Comments to: webmaster@geom.umn.edu
Created: Thu Jun 25 15:09:39 CDT 1998 --- Last modified: Thu Jun 25 15:09:39 CDT 1998