User:Hasil Lombard/Spheremid

A Spheremid has four vertices and no facets. An interesting fact about the spheremid (and morphed or stretched variations of it) is that, unlike any other shape but the cylinder, it rolls in a predictable way. Among the illustrations below is one comparing the path of the spheremid to that of the cylinder.

Steve White, of New York City, discovered this shape in 1971. He took models and drawings of it to a company that specialized in patent application and market research; with the naïve idea that they could quickly get patent pending status and then approach a certain toy company that he felt certain would want it. By the time it appeared in the next catalog of that same company (without Mr. White's knowledge), he discovered that the invention research and marketing company was being investigated by the Attorney General; and was being sued by many irate clients. Many years later, he discussed this with someone who was very excited about the prospect of showing it to a friend who worked for a very large and prestigious jewelry firm. The idea was to cast this shape in precious metals. Many months later, Mr. White got a call from this person’s partner, who asked if he had seen the Sunday Times. Sure enough, he found an article about this same company’s introduction of something they called a “Step Mace,” which was the spheremid! The caller further mentioned that her (former) partner had “disappeared” months earlier. Mr. White did another project for them several years later, and the two remaining partners claimed that they still had no idea what became of their former partner.

Many years later, there was an article in Scientific American magazine about this shape, and a follow-up article due to reader response. One of the readers had written in to say that he had patented this shape back in 1981. I include all these anecdotes and coincidences only to give as complete a history of the spheremid as I can.

The Spheremid is a symmetrical solid. It is formed as follows: 1: Starting with two identical isosceles 90 degree cones, the cones are bisected and: 2: Bonded at the base so that each has two sides. One side is flat and square and the other appears as two cones, base to base. 3: Put the flat sides together so that you have two cones base to base. 4: Holding one stationary, rotate the other side 90 degrees. This forms the Spheremid.

Although there are other ways to arrive at this shape, such as removing material from a sphere or a cube, I believe this is the simplest approach.