
The facets are the two smooth front surfaces which have been cut and polished to make them smooth. It is probably a bit lumpy on the other side, that would be from when the final round blown hot blob of glass on the end of the blowing iron (pontil rod) containing all the colours is taken to a flat cold metal surface (called the marver) and pressed against it to make this lollipop shape.
It would have been pressed to the marver twice to make the angle on the front, once on the back to make it flat.
Then the angled side (and the base) is cut and polished, cold-worked, not hot worked.
That is labour intensive stuff.
It's just called a "Ice-cut lollipop". Presumably because after cutting, you can see clearly through the glass, like good, clear, sharp ice.
Lollipop, I suspect, just describes the shape - round and flat, with a stick bit.

They did make lollipops without this double flattening into an angle on one side, so the name is to distinguish what sort of Lollipop it is.
This can be further confused, by the lollipops which were shaped to be "Cut-ice" ones, but somehow ended up on the shop shelves without being cut and polished, so the surfaces are not all smooth.
Theoretically, that would be an "uncut Ice lollipop"
Early on, how well something got finished off, or whether Mdina was written on the bottom, depended very much on how much stock was on the shop shelves and if somebody was available to do the "finishing-off bits" of work.
If the shelves were empty and nobody was available, unfinished-off work got sold.
It was really, really popular, right from the start. They had trouble keeping up with having enough stock to sell.
I'm all pleased for you that you really have got a treasure here. That is always a big bonus on top of liking it.
