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Pyrite forms cubic crystals, both in theory and in nature:

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However, the noble metals, like silver, that have cubic, face-centered lattices, do not seem to form cubic crystals in nature.

One possible explanation is that silver and other noble metals are invariably contaminated by trace amounts of other elements that prevent perfect crystal formation. For example, salt (NaCl) is also cubic, and when very pure deposits of salt are found, they may have large cubic crystals, but normal salt generally does not form such crystals presumably because of contamination.

Is this the explanation why gold and silver do not form cubes when they solidify? If so, imagine we somehow obtained perfectly pure silver as a gas or liquid, would it crystallize on cooling to a cube?

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Native silver crystals can be found in cubic, octahedral, or dodecahedral forms. As you mention, silver often is found with gold, copper and other metals, and with gold, tends to hexagonal stacking, rather than cubic crystals.

Silver may also form pseudomorphs, in which the crystal shape is from its progenitor or its surroundings. For example, dyscrasite, $\ce{Ag3Sb}$, or acanthite, $\ce{Ag2S}$ may be replaced by silver in the form of the antimony or sulfur minerals.

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