meet the Octacube

This is the Octacube, a 6′X6′ sculpture installed at the Penn State campus. It was comissioned by a mathematics alumna in honor of her husband, who was killed in the attacks on the World Trade center. It was created not by a professional artist, but, amazingly, by a Penn State math prof (Adrian Ocneanu) and the Penn State Engineering Services Shop.

This gorgeous piece of mathematical sculpture 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.”

The Octacube “maps the four-dimensional solid into a space perceptible to the human observer. [Ocneanu's] process, radial stereography, presents a new way of making this projection. He explains the process by analogy to mapping a globe of the Earth onto a flat surface. ‘We place a light bulb at the north pole of the Earth and we project onto a sheet of paper placed underneath it,’ he says. ‘The southern hemisphere, away from the north pole, will remain quite small, while the northern hemisphere, near the projection pole, will become very big and north pole itself will be sent toward infinity.’ The technique can be used to make a two-dimensional projection of a cube by first mapping the cube radially onto the surface of a globe. Ocneanu explains, ‘The edges of our cube become circles on the map, just like straight highways are slightly curved on maps of the Earth. Its angles, however, remain true in this projection, so the map retains the key aspects of the symmetry of the original cube, unlike a photograph of a cube.’”

Don’t miss this animation of the sculpture or this animation of a hypercube rotating in four dimensions as envisioned using windowed radial stereographic projection.

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