Octacube (sculpture)

The sculpture was designed by Adrian Ocneanu [de], a mathematics professor at Pennsylvania State University.

Octacube was funded by an alumna in memory of her husband, Kermit Anderson, who died in the September 11 attacks.

Discussing the construction, Ocneanu said:[1] It's very hard to make 12 steel sheets meet perfectly—and conformally—at each of the 23 vertices, with no trace of welding left.

In some cases, the mirror-like surfaces create an illusion of transparency by showing reflections from unexpected sides of the structure.

There are subtle optical effects that you can feel but can't quite put your finger on.The Platonic solids are three-dimensional shapes with special, high, symmetry.

An analogy for converting the 4-D 24-cell into its 3-D sculpture is cartographic projection, where the surface of the 3-D Earth (or a globe) is reduced to a flat 2-D plane (a portable map).

All of them have limitations in that they show some features in a distorted manner—'you can't flatten an orange peel without damaging it'—but they are useful visual aids and convenient references.

Some, but not all, of the symmetry elements are Using the mid room points, the sculpture represents the root systems of type D4, B4=C4 and F4, that is all 4d ones other than A4.

Sulfur hexafluoride (or any molecule with exact octahedral molecular geometry) also shares the same symmetry although the resemblance is not as similar.

The subject has been described by a Fields medal winner, Ed Witten, as the most difficult area in physics.

[2] Part of Ocneanu's work is to build theoretical, and even physical, models of the symmetry features in QFT.

[1] Summarizing the memorial, Anderson said:[1] I hope that the sculpture will encourage students, faculty, administrators, alumnae, and friends to ponder and appreciate the wonderful world of mathematics.

I also hope that all who view the sculpture will begin to grasp the sobering fact that everyone is vulnerable to something terrible happening to them and that we all must learn to live one day at a time, making the very best of what has been given to us.

It would be great if everyone who views the Octacube walks away with the feeling that being kind to others is a good way to live.Anderson also funded a math scholarship in Kermit's name, at the same time the sculpture project went forward.