Zocchihedron

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The Zocchihedron is approximately 1.5 inches (38 mm) in diameter

Zocchihedron is the trademark of a 100-sided die invented by Lou Zocchi, which debuted in 1985. Rather than being a polyhedron, it is more like a ball with 100 flattened planes. It is sometimes called "Zocchi's Golfball."

Zocchihedra are designed to handle percentage rolls in games, particularly in role-playing games.

[edit] History

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 is a further improved model, and has a different filling material.

[edit] Probability distribution of rolls

A test performed for White Dwarf magazine concluded that the frequency distribution of the Zocchihedron was substantially uneven. Jason Mills performed 5,164 rolls^[1] and found that results greater than 93 or less than 8 are significantly rarer than intermediate results. Mills attributed this to the placement of the extreme numbers near the poles of the zocchihedron, where they are closer together. Numbers near the equator are more widely spaced.

Later versions of the Zocchihedron have been designed with a different pattern of number distribution, resulting in more even results overall. Individual numbers still suffer from the bias.^{[citation needed]}

[edit] Patents

The aesthetic appearance of the Zocchihedron was protected by United States design patent D303,553, which expired on 19 September 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 on 9 August 2025 and applies only to 100-sided dice containing "multi sized and irregularly shaped particles."

[edit] Notes

1. ^ Binomial distribution dictates that, to be confident of an average result on a fair die, the number of trials required is the mean divided by the probability of a given result. Here the mean is 101/2 and the relevant probability is 1/100, so the number of trials required is 5050.