If the basic polygons are cells of a regular tiling of the plane by squares, equilateral triangles or regular hexagons, then the polyform is called a polyomino, polyiamond or polyhex respectively.
In Sections 6 and 7, we find the threshold sequence for each polyiamond and polyomino of size smaller than 5.
Unbiased polyiamond games are studied in [4, 5, 8].
were named and popularised by Thomas H.
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 (Figure 3).
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.
If each player uses a coloured set of all polyiamonds from the moniamond to the hexiamonds, what size hexagonal triangle-grid board would be suitable to fit all the pieces, 22 of each colour?