Chelona Pocket Puzzle - Cats A nine-square edge matching puzzle from Chelona in Greece. Novel packaging - an extra backing tile has an attached elastic cord to enclose the stacked tiles. Eternity II employs 256 square tiles to be arranged in a 16x16 grid, which must have a gray border and a particular tile at a given "starting" position.
The "final scrutiny date" passed without a winner, so the prize went unclaimed.
There are many modern edgematching puzzles - you may have heard of "Scramble Squares" for example.
Jacques Haubrich published his definitive Compendium of Card Matching Puzzles in three volumes, in which he describes over 1000 puzzles, and a companion volume called About, Beyond, and Behind Card Matching Puzzles in which he provides interesting theoretical and historical analyses. Richards doesn't claim the triangular form of the dominoes, but rather the ways to make and mark them.
Tile-laying puzzles (in German, "Legespiel") of both the edge-matching and polyform varieties have been explored and produced by Kate Jones at Kadon, and you can read a lot of interesting material at the Kadon site - see Edgematching Colors and Shapes, and More About Edgematching. You can see some original designs by Yukio Hirose here.