The 16 Coated Amethysts are ingredients for the Amethyst Multishard - which itself crafts the Megacake.
There's 4 extra secret bonus Coated Amethysts that aren't related to the Amethyst Multishard.
All amethysts are obtained by combining 1 Amethyst Shard with 1 specific material at a Lapidary Table.
The Lapidary Table is crafted with 1 Amethyst Block, 1 Opal Core, 1 Polished Rhyolite, and 6 Quartz Blocks.
Lapidary table interface:
The list of possible combinations are listed on the Lapidary Table's List of fusables
menu.
The 4 secret ones are SECRET. You can read about them at the bottom of this wiki page if you don't care about spoilers.
Combine all 16 main Coated Amethysts at an Amefuser to obtain the
Amethyst Multishard. Wielding the Multishard gives the
Multishine advancement.
Amefuser recipe:
Amefuser interface:
(each slot corresponds to a Coated Amethyst Shard)
Here's all the SECRET Lapidary Table recipes: