What

This is a game, called Liberation, which is an approximation of Chinese chess on a board that represents an exotic mathematical surface – the Projective Plane. It is an approximation of Chinese chess because some alterations of the game were required in order to accommodate the odd space.

How

It is played as if the opposing edges are joined together, with a twist. That is, if a piece is pushed off the left edge near the top, it will appear on the right edge near the bottom, and likewise for the top and bottom edges. It is not possible to physically join all opposing edges together in this fashion, in three dimensions. The player soon feels as if he or she is conversing in an impossible space, much like the characters in the story, "Alice Through the Looking Glass". By joining the opposing edges with a twist, the opposing corners, that is the ones diagonal from each other, are fused together. The two black spots are considered to be one, a kind of singularity that defies comprehension, like a black hole, and likewise with the two red spots. Since there are no edges, each army must be arrayed around a point, that point being one of the singularities.

It is not necessary to understand the space, or even how pieces are allowed to move, in order to play the game. If a piece is on the board, holding the mouse down on it will highlight all the points to which it is allowed to move. If its target point is not one of the highlighted points then the move will be rejected. In Chinese chess, some pieces, namely the General (Jiang4 or Shuai4), the Administrator (Shi4) and the Elephant (Xiang4), are confined to a limited set of points. When placing any of these on the board, if the target is not within the permitted domain then the move is rejected. If the player happens to be setting up an arbitrary deployment and needs to change a foot soldier's direction, the player can toggle through the foot soldier's available directions by making it current by clicking on it, and then toggling through via the spacebar. If a piece will not go where intended because the target is illegal from where it is, the piece can be cleared simply by removing it from the board. The intended target should now be legal for the piece fresh from the box, if the target is within the piece's permitted domain.

In regular Chinese chess, the foot soldier (Zu or Bing) can move ahead until it has crossed the river, whereupon it is allowed to also sidestep, but not move backwards. In an edgeless space that is oddly twisted so that the river must cut in two directions in order to divide it, the foot soldier at first may move only toward the closest point(s) on the riverbank. If the foot soldier initially happens to be equidistant from two branches of the river then it will have a choice at first of which way to go. After it has crossed the river, it may move in its now established dominant direction in orbit around the enemy singularity. It may sidestep, but only if the orbit remains the same or tightens. In other words, once the foot soldier has crossed the river, the distance between the foot soldier and any branch of the river may not decrease.

To help the player keep track of the foot soldier's direction, it has a directional image. That is there is a dot on the foot soldier that points in the direction it is allowed to move. As mentioned before, the foot soldier's dominant direction can be changed.

Rules

Jiang4 (black), Shuai4 (red): the General; moves one step at a time, orthagonally within a limited compound. In regular Chinese chess the compound has 9 points. In Liberation these points have collapsed into 6. In Liberation, the General's starting point is marked with a tiny white square.

Shi4 (black), Shi4 (red): the Administrator; moves one step at a time, diagonally within the same compound as the General. In Liberation each of a colour's two Administrators travels on an independent path from the other, within the General's compound.

Xiang4 (black), Xiang4 (red): the Elephant; moves diagonally two steps at a time, but may not jump over any piece. The Elephant cannot cross the river, hence its permitted points are limited to 7 in regular Chinese chess and 12 in Liberation. Its points are marked with crosses.

Ma (black), Ma (red): the Knight; moves one orthagonal step then one diagonal step, but only if the orthagonal step is not occupied.

Ju (black), Ju (red): the Chariot; moves any number of steps in a straight line.

Pao (black), Pao (red): the Artillery; moves any number of steps in a straight line, but can kill only if there is an intervening piece between it and its target.

Zu (black), Bing (red): the Foot Soldier; moves one step at a time straight ahead, until it has crossed the river, whereupon it may also sidestep (move one step perpendicular to its forward direction). In Liberation, forward means toward the river before crossing, and away from the river after crossing. In Liberation, the Foot Soldier's starting points are marked with tiny grey squares.