The Sphericon

The sphericon was found by Colin J. Roberts, of Baldock, England, while attempting to carve a Möbius strip without a hole in the middle from a piece of Mahogany. He was pleased with the result, gave it to his sister, and thought no more of it. In the late 1990s, he became interested in sphericons once more and began thinking about their properties.

He constructed hundreds of sphericons out of cardboard, and investigated how they can be arranged. He also devoted much time to thinking about other variations on the theme, and with his son (and author of this website) Paul, came up with an infinite series of sphericons.

In October 1999, Ian Stewart wrote an article "Cone with a Twist" on the subject in his Mathematical Recreations column of Scientific American. This sparked quite a bit of interest in the shape, and has been used by Tony Phillips of State University of New York at Stony Brook to develop theories about mazes, is used as a logo and name by the Israeli research company Sphericon Ltd, and is even used as a centre-piece for a cultish ritual.

There's a good page about the sphericon family here, a Wikipedia article here, and a Wolfram page here.

The Oloid is a geometric shape created separately by the German sculptor Paul Schatz. It is like an elongated sphericon that has the same volume as a sphere. It is useful for mixing and aerating.