The BCNM Icon

The BCNM icon is a 3D solid known as a Meissner Tetrahedron.

We want it to convey both the future and the past. We started by thinking about the Greek letter Delta, an equilateral triangle that in mathematics denotes "change". We were also thinking of the Borromean knot used illustrate the three interlocking primary elements of the BCNM: Humanities, Art and Design, and Technology.

As a Delta gets inflated, it becomes a Reuleaux triangle, a 2D curve of constant width used on some applications of robotics (and is the rotor in the Wankel/Mazda Rotary Engine). When extended to three dimensions, the Reuleaux triangle becomes a Reuleaux tetrahedron, a solid common to four spheres of equal radius placed so that the center of each sphere lies on the surface of the other three. The centers of the spheres are located at the vertices of a regular tetrahedron, and the solid resembles an inflated tetrahedron with four curved edges [1,2].

As noted by Weisstein and by Lachand-Robert and Oudet, the Reuleaux Tetrahedron is not a spheroform, a solid of constant width. However Ernst Meissner showed in 1911 how to modify it to get a body of constant width called the Meissner Tetrahedron [3].

1. Weisstein, Eric W. "Reuleaux Tetrahedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ReuleauxTetrahedron.html
2. http://en.wikipedia.org/wiki/Reuleaux_tetrahedron
3. Spheroforms, with link to "Bodies of constant width in arbitrary dimension", by T. Lachand-Robert & I. Oudet: http://www.lama.univ-savoie.fr/~lachand/Spheroforms.html

Jaron Lanier's version (Spring 2008)

Michael Joaquin Grey's version (Spring 2008)