Zocchihedron

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Zocchihedron is the trademark of the most common 100-sided die, invented by Lou Zocchi, which debuted in 1985. It is not a polyhedron. Rather, it is more like a ball with 100 flattened planes. It is sometimes called "Zocchi's Golfball."

It took three years for Zocchi to design his die, and three more years to get it into production. Zocchi discovered that the die would perform best at a thickness of 13.85 mm. Since its introduction Zocchi has improved the design of the Zocchihedron, filling it with teardrop-shaped free-falling weights to make it settle faster when rolled. The Zocchihedron II has recently been released. It's a further improved model, and has a different filling material.

Zocchihedra are designed to handle percentage rolls in games, particularly in roleplaying games. They are not in common usage because of their unwieldiness (the original Zocchihedrons take several seconds to settle), their scarcity, and their cost (a single 100-sided die will typically cost as much as perhaps 10 or 20 regular dice). Players often find it more convenient to use two ten-sided dice (or two 20-sided dice) numbered 0–9 of differing colors, in advance declaring one color as the "tens" die and the other as the "ones" die; there are also ten-sided dice marked 00 to 90 using intervals of ten, which can be combined with a regular ten-sided die marked 0 to 9 to the same effect.

[edit] Probability distribution of rolls

A test performed by Jason Mills for White Dwarf magazine concluded that the frequency distribution of the Zocchihedron was substantially uneven, 5,164 rolls (binomial distribution dictates that to be confident of an average result on a fair die the number of trials required (n) is equal to μ ÷ p, where μ = mean, or die average, and p = probability of a single result. n = 5050 for a d100) led Mills to conclude that results greater than 93 or less than 8 are significantly rarer than results between these figures. Mills attributed this to the especially high, and especially low numbers being situated at the poles of the sphere — and thus being closer together. Numbers near the equator are more widely spaced.

It is important to note that this test was conducted in 1987, a mere two years after the release of the Zocchihedron. The Zocchihedron II, which features orderless number distribution and even spacing may be fairer.

[edit] The Zocchihedron patents

The aesthetic appearance of the Zocchihedron was protected by United States design patent D303,553 which expired September 19, 2003. There was never a utility patent for the original Zocchihedron, although United States patent 6,926,276 may protect the braking mechanism of the Zocchihedron II. That patent will expire August 9, 2025 and applies only to 100-sided dice containing "multi sized and irregularly shaped particles."