2.3 Tiers

The board is divided into four Tiers (or ``levels''), each of which constitutes an implied square on the playing board. The descriptions in the rest of this section refer to Figure .

Figure: An Illustration of the Game's Four Tiers

2.3.1 Center Tier

A space is said to be in the Center Tier if the center of the board is one of its corners. The Center Tier contains sixteen spaces.

2.3.2 Second Tier

Any space which is not in the Center Tier, but which shares all of its corners with some space sharing at least one corner with a space in the Center Tier is said to be in the Second Tier.

Formally, for a space $S$, $S$ is in the Second Tier if and only if for every point $p$ which is a corner of $S$, there exists a point $p^\prime$ and spaces $S_p$ and $S_p^\prime$ such that $p$ is a corner of $S_p$, $p^\prime$ is a corner shared by both $S_p$ and $S_p^\prime$, and $S_p^\prime$ is in the Center Tier. In most cases, $S_p = S$.

The Second Tier contains thirty-two spaces.

2.3.3 First Tier

A space is said to be in the First Tier if it is neither in the Center Tier nor in the Second Tier, and if it shares at least one corner with some space in the Second Tier. The First Tier contains thirty-two spaces.

2.3.4 Rim

A space is said to be a member of the Rim Tier, or ``on the Rim'' if one of its borders is an edge of the board itself. The Rim contains twenty-four spaces, four of which also belong to the First Tier. These four triangular spaces are known as ``ambiguous'' spaces.