# 4th-Dimension Gift In Memory of Her Husband Killed on 9-11

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** The Octacube **by

**Adrian Ocneanu**

A Point in 4th-Dimensional Space

"The sculpture is a gift from Jill Grashof Anderson, a mathematics alumna of Penn State as a memorial for her husband, Kermit C. Anderson, also a Penn State mathematics graduate, who was killed in the terrorist attack on the World Trade Center in New York City on 11 September 2001.

The dedication ceremony for the sculpture included an explanation of its mathematical meaning by its designer, Adrian Ocneanu, professor of mathematics. Ocneanu is a mathematics researcher who works on models of Quantum Field Theory based on symmetry.

The sculpture is titled * Octacube* as its 24 vertices consist of the 16 vertices of the 4 dimensional cube, also known as hypercube or tesseract, together with the centers of its 8 rooms, which form the vertices of the 4d octahedron.

The sculpture, which measures about six feet in every direction, presents the three-dimensional * shadow* of a four-dimensional solid object.

Ocneanu designed the sculpture as a research and teaching tool related to his research. The stainless-steel Octacube is a striking object of visual art and also a mental portal to the fourth dimension, a teaching tool, and a research object bringing together many branches of mathematics and physics connected to the structure of symmetry.

Although mathematicians can work with a fourth dimension abstractly by adding a fourth coordinate to the three that we use to describe a point in space, a fourth spatial dimension is difficult to visualize, Ocneanu explains.

Ocneanu wrote the software which gave the cutting instructions for 1/8" stainless steel sheets to the machinists in the Penn State Engineering Shop. The machinists then worked for almost a year to bend into spherical shapes and weld the 96 triangular pieces which meet in a giant puzzle, 12 at each of the 23 vertices of the sculpture - the 24th vertex is at infinity. The sculpture measures 6 x 6 x 6 ft and weighs 1200 lbs."