Mechanic #135  Tessellation Tactics 
 Posted: 12/09/11
A tactical game made with nonuniform, tessellating cells. 
Fig 135.1  Image borrowed from here.
Have you every wondered why tactics games tend to have grids mad up either squares or hexagons? Because there are only three regular polygons that tessellate perfectly: hexes, squares, and triangles. If you want to have a uniform field of cells, then you need to pick one of these three shapes. Triangles are rarely picked, presumably due to the limited tactical options.
Fig 135.2  Also borrowed from here.
But what if you don't want a symmetrically tiling tessellation? What if you make having tessellations made up of a variety of different shapes part of the gameplay? That would make for some unique looking game boards! But you'd need a set of rules that defined how the different polygons interacted.
First off, I'm going to assume that the tessellated segments are all convex polygons. They are polygons rather than free form shapes because I'm going to use edges to dictate facing, and they are convex because attacks can only come from one direction. Concave polygons can border a neighbor shape on more than one edge.
The general rule of thumb is that a unit can only be in a single cell at any one time. The unit's base must fit completely within the cell. Also, one of the edges is considered the facing of the unit. Attacks from behind will do more damage, so in order to decide what constitutes "behind" on a oddly shaped polygon, when need to know where the front is, and count backwards.
Because of the nature of nonsymmetrical tessellations, you usually end up with a severe difference in size between the polygons that make it up. In the following example, the triangle cells are much smaller than the square cells. To make things interesting, I think it would be neat if more than one unit can occupy a larger cell.
Fig 135.3  Nonstandardized unit sized.
Here, we've got a disparity between the red and blue sides. The blue units can only move along a single line, so there must be some sort of movement rule to facilitate that (Chinese Checkerslike hopping, for example). The red units are much smaller, both in size and presumably power. They can only fit a single unit per triangle, but two units in the squares. In Tessellation tactics, polygons are attacked, not individual units. So, if B attacks a square with two A units, it will end up attacking both of them. Similarly, in each turn for both the A units in a square, they would both attack B.
Fig 135.4  Nonstandardized movement units.
For great differences in size, you can even consider the tessellated shapes to make up other tessellated shapes. In this example, the small, red A units can sit on all of the cells except the triangles. So A is using individual cells for movement. However, B is huge, and considers movement based on collections of polygons. In this case, it is roughly the size of the 12sided figure (a dodecagon?) made up of the hexagon, six squares, and six triangles. Presumably, there'd only be one big B on the board, since the multicell spots overlap, causing movement difficulties if they get too close together.
The basic idea here is that irregular tessellations yield different sized shapes and patterns, which could be employed to build unique gameplay opportunities.
As you break away from hex and square tessellations, you lose the ability to count edges for line of sight. Even triangles, which are symmetric tessellations, do not have straight lines from the middle of one edge to another four cells away. Simply put, if you want line of sight rules, you can not rely on the board to deliver simple and obvious answers.
The easiest solution is to do what miniature games have been doing forever. Just draw an imaginary line from the center of one cell to the center of the destination cell and see if it crosses a cell which blocks line of sight. This can lead to arguments when it is not clear whether a cell is being crossed or not, so a simple addition to the rule is that if you can draw an imaginary line from any vertex on the source cell to any vertex on the destination cell without clearly crossing a blocking cell, you have line of sight.
Finally, we have rules for facing. Generally speaking, tactics games tend to reward players for outmaneuvering the enemy by having hits done from the flank or from behind cause more damage. This helps alleviate the problem of players just rushing up to his foe and sitting in one spot rolling dice or whatever until the enemy is dead. It rewards spatial thinking, and adds tactical options as you try to get your foes to look at that three headed monkey behind them.
But how do you represent something like that in a game with cells that have a variable number of edges. Simple. Each edge represent a percentage of these total number of edges. So, for a square, each edge is worth 25%, while in a pentagon, 20%, a hexagon, 16.7%, and so on. Count the number of edges from the front and multiply it by 2 (since the back is halfway around from the front).
Fig 135.5  Edge values for facing polygon.
Here, we've got a hexagon. Each edge is worth 16.7%, but to make things simple, I've just made two thirds of the edges 17%. To calculate damage increase, just add up the sides from the front facing edge and multiply by two. If you were behind the hex, you'd count three sides  17% + 17% + 16% = 50% * 2 = 100%. So, you'd do 100% more damage from the rear face (or 100% of the possible extra damage). If you add more edges, each edge is individually less powerful, but the result would be the same. The closer you get to behind, the more extra damage you would do.
