"Amethyst and Quartz slices with Agate center".
This name would be better than Amethyst Stalactite slices.
Stalactites and stalagmites developed and are still developing in LIMESTONE CAVES and thus are limestone formations, nothing to do with quartz formations.
Sometimes columns of amethyst and/or quartz crystals formed inside amethyst geodes, often accompanied with spectacular calcite crystal formations.
Many of the larger Uruguayan amethyst geodes are too big for many collectors, as space is often an issue.
The clusters, or single columns of amethyst are with great care removed from the inside of these geodes by destroying the geodes.
Of course that small part of the geode itself ,from where these columns have developed is the base of the newly created specimen.
It happens sometimes that some columns break during the delicate operation.
These broken columns now are sliced into 4 to 5 mm thick pieces, polished on two sides and sold individually to the jewelry industry and the larger ones to the mineral collectors.