Amethyst Shard

An amethyst shard is a crystal obtained from mining a fully grown amethyst cluster or can be obtained from chests in ancient cities.

Mining
An amethyst cluster mined using a non-Silk Touch, non-Fortune pickaxe drops 4 amethyst shards. When mined using any other tool, item or mechanism (such as explosions or pistons) it drops 2 shards. The maximum amount of amethyst shards dropped can be increased with Fortune. Fortune I gives a $1/3$ chance for eight shards, averaging 5.33 shards; Fortune II gives a 25% chance (each) to give eight or 12 shards, averaging 7 shards, and Fortune III gives a 20% chance (each) to give 8, 12, or 16 shards, averaging 8.8 shards.

If the amethyst cluster in any of its growth stages is mined using any tool enchanted with Silk Touch, it drops itself rather than amethyst shards.

Allay duplication
If an amethyst shard is given to an allay that is currently dancing to an active jukebox, the allay emits heart particles, consumes the amethyst shard and duplicates into another allay. After this, there is a 5 minute cool down until both allays can be duplicated like this again.

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Trivia

 * Although in real life is a variety of  like nether quartz, the two resources are not interchangeable.