Glass fragments bedded on clear epoxy atop a white base looked OK, albeit minus most of their glitter due to epoxy filling their cracks:
Filling the cracks with black epoxy makes them stand out:
So I assembled a coaster from shattered glass in a clear surround with black epoxy atop a mirror base:
Each fragment sits on a blob of black epoxy that eventually oozed out to fill the gap between the mirror and the transparent layer. You can see the oozing start around the two fragments in the upper left.
A top layer of black acrylic sits flush with the upper surface of the glass, seen here with the protective paper in place before pouring black epoxy into the gap around the perimeter of each fragment:
Peeling the paper away exposes an almost perfect surface, with the epoxy forming a slight curve between the black acrylic and the glass:
The mirror doubles the number of glass cuboids and their glittery gaps:
All in all, it turned out well, but the epoxy pouring and leveling is tedious.
It might be possible to assemble a coaster upside-down, with the black layer stuck to something like Kapton tape and the fragments carefully aligned in their openings to make the entire top surface a plane. The tape should keep the epoxy from oozing out of the gaps, although a perfect seal may be impossible.
Then fill the gaps with black epoxy, lay the clear middle layer in place, run a dollop of epoxy on each fragment, lay the mirror in place, and hope there’s enough epoxy to fill all the gaps and not enough to make a mess around the perimeter.
With a bit of luck, that wouldn’t require so much hand finishing.
The next coaster must have a perimeter shrinkwrapped around the fragments, if only to break the low-vertex-count polygon tradition.