Gemblo is one of the possible polyhex games that might be invented.
In the two-player version of the game, players use the rules for a standard 4-player game, with each player taking a set of polyhex pieces of two colours, and alternating turns: Player-1-colour-A, Player-2-colour-B, Player-1-colour-C, and so on.
Alternatively, three players could follow the 2-player approach, with each player taking a set of polyhex pieces of two colours and in a player's successive turns placing a piece of one, and then the other, of their two colours.
Except in the case of the two-player version, each player has an identical set of eighteen polyhex pieces in a unique colour: 8 pentahexes; 5 tetrahexes; 3 trihexes; 1 duohex; and, 1 monohex.
Caption: Figure 2: Example of the 18 Gemblo polyhex shapes in one colour.
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.
Polyhex achievement games are studied in [3, 20, 22].
ABSTRACT: A toroidal polyhex is a cubic bipartite graph embedded on the torus such that each face is a hexagon.
Key Words: ful lerene, toroidal polyhex, super edge-antimagic total labeling.
A toroidal polyhex (toroidal fullerene) is a cubic bipartite graph embedded on the torus such that each face is a hexagon.
Preliminaries for toroidal polyhex Let L be a regular hexagonal lattice and n P m be an mxn quadrilateral section (with m hexagons on the top and bottom sides and n hexagons on the lateral sides, n is even) cut from the regular hexagonal lattice L.
Cash, Simple means of computing the Kekul'e structure count for toroidal polyhex fullerenes, J.