We might think laterally and link the word 'tile' with polyominoes, or polyiamonds
, as in Solomon Golomb's game of pentominoes, or variants of Blokus.
The result is a game that uses polyiamonds
(the polyomino-like family of two-dimensional shapes, built using unit-sided equilateral triangles) to make a set consisting of all the mathematically distinct polyiamonds
, from the unique moniamond to all of the hexiamonds.
Find all the mathematically distinct polyiamonds up to six triangles at a time: moniamonds, diamonds, triamonds, tetriamonds, pentiamonds, and hexiamonds.
Similarly, Blokus has been adapted into Blokus Trigon for 4 players, each using a coloured set of all the polyiamonds up to hexiamonds, on a hexagonal triangle-grid board.