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.
Figure 1b shows that the polyiamond [T.sub.3,1] is a (2,5)-winner using the strategy of Proposition 2.2 with h = [delta] = 3.
Unbiased polyiamond games are studied in [4, 5, 8].
Blokus--using squares--has a sistergame called Blokus Trigon that uses polyiamonds
, those families of shapes made from unit-sided equilateral triangles joined whole-edge to whole-edge.
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).
(Changing a mathematical situation by altering a building block is one version of problem-posing.) 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.
In both of these 2-D versions of Blokus, each player has a set of pieces (polyominoes, or polyiamonds) of one colour.
O'Beirne's further generalisation to Polyiamonds. The traditional word "domino" for a two-square shape, suggested using "do-" (like "duo") and "-omino" to create a number-word family of ominoes.
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?