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Snowflakes that look identical, but may vary at the molecular level, have been grown under controlled conditions. [12] Although snowflakes are never perfectly symmetrical, the growth of a non-aggregated snowflake often approximates six-fold radial symmetry, arising from the hexagonal crystalline structure of ice. [13]
Capped 6-sided long die: Two six-faced long dice are used to simulate the activity of scoring runs and taking wickets in the game of cricket. Originally played with labeled six-sided pencils, and often referred to as pencil cricket. 7 Pentagonal prism: Similar in constitution to the 5-sided die. Seven-sided dice are used in a seven-player ...
Crazy dice is a mathematical exercise in elementary combinatorics, involving a re-labeling of the faces of a pair of six-sided dice to reproduce the same frequency of sums as the standard labeling. The Sicherman dice are crazy dice that are re-labeled with only positive integers .
When snowflakes crystallize, they do not touch each other. Thus, snowflakes form euhedral, six-sided twinned crystals. In rocks , the presence of euhedral crystals may signify that they formed early in the crystallization of liquid magma or perhaps crystallized in a cavity or vug , without steric hindrance , or spatial restrictions, from other ...
A set of polyhedral dice. Platonic solids are often used to make dice, because dice of these shapes can be made fair. 6-sided dice are very common, but the other numbers are commonly used in role-playing games. Such dice are commonly referred to as dn where n is the number of faces (d8, d20, etc.); see dice notation for more details.
For instance, the six-sided die could have abstract symbols rather than numbers on each of its faces. Less simply, a random permutation is a permutation generated uniformly randomly from the permutations of a given set and a uniform spanning tree of a graph is a spanning tree selected with uniform probabilities from the full set of spanning ...
Consider the following set of dice. Die A has sides 2, 2, 4, 4, 9, 9. Die B has sides 1, 1, 6, 6, 8, 8. Die C has sides 3, 3, 5, 5, 7, 7. The probability that A rolls a higher number than B, the probability that B rolls higher than C, and the probability that C rolls higher than A are all 5 / 9 , so this set of dice is intransitive. In ...
Diceware is a method for creating passphrases, passwords, and other cryptographic variables using ordinary dice as a hardware random number generator. For each word in the passphrase, five rolls of a six-sided die are required. The numbers from 1 to 6 that come up in the rolls are assembled as a five-digit number, e.g. 43146. That number is ...