The standard positions (std0*) are not supposed to make sense from a sportive gaming point of view, but simply provide all types of pieces for testing purposes. Of course the really interesting positions are yet to be found - contributions are welcome!
For every party, the piece having the king role is indicated by a magenta 'circle' shape around it. That specific color was used for royal clothes in the middle-age and so is most suitable for our purpose.
The pieces can move as described in Table 3.1, “Piece Moving Rules” (in the GUI keep the SHIFT key pressed, select the piece and then the desired new location with a left mouse click). At the moment the implementation of piece E is missing in the GUI (it would require two clicks).
Table 3.1. Piece Moving Rules
| type | rule |
|---|---|
| A | 1 step to a neighboured face |
| B | like A, but infinitely many subsequent steps, having +-1 edge between last and next visited face |
| C | like B, but only 1 move with distance of 2 steps (jumping) |
| D | like A, but only one direction, direction evolving with +1 edge (counter-clockwise) in between |
| E | like D, but no restriction upon the next direction |
| F | like B, having +2 edges in between (asymmetric) |
| … | … |
On one hand there are well-definable moving rules, on the other there exist unique ways to make up visual representations for the pieces.
The mapping
Because visuals tell more than thousand words, Figure 3.3, “Chess Piece Type C” demonstrates how a piece of type C can move.
Figure 3.3. Chess Piece Type C
About how a piece of type C can move on a board with hexagons (best seen in colour).
In the following picture (see Figure 3.4, “Chess Piece Type F”) you see how a black piece F can move while another piece, a red A, coexists. The two pieces have been placed onto green faces for didactic purposes only. The blue lines represent directed ways the piece F can travel along.
Keep in mind that it's an asymmetric case this time (and so the visual representation does of course indicate that), but this only becomes measured as soon as another piece enters the scene and starts disturbing, that is to say the blue line showing how the red piece can be captured is not in effect behind the face occupied by the red piece, and so the face between the two pieces wouldn't be reachable by the black F within a single move if it wasn't along another line.
Figure 3.4. Chess Piece Type F
A piece of type F on a board of pentagons whilst showing the effect of a second piece.
One word of caution: One should ensure (for example) that in case where a moving rule definition collapses (or becomes unclear) in a special case (e.g. poly=3 or others), the correspondent (mapped) visualization rule should collapse (or …) as well. This field is still under construction and therefore things will certainly change over time. For example, the piece F (with distIE = +3 asymmetric) moving rule becomes symmetric in case of poly=6 (for 3 = 6 - 3), but the current visualization stays asymmetric, so it's not perfect at the moment.
Btw. those movement lines look like geodesics and a torus knot or link thing! See the Chapter 10, Knots and Links chapter for more information. Or, actually it strongly resembles the curl-free (Pólya) vector potential field (rot grad = 0), and we have no problem with considering a related picture for the div rot = 0 (just draw lines along faces of same distance from the piece origin, this has to do with theta series as well).
Rules are adopted from Chess. Pieces with a royal role should be taken special care of (see Figure 3.5, “After a Checkmate”).
We do not stop in case of a mate position but require the king to be captured. At most one piece may be located at a given space/time. Piece D is not transmutating (promotion) nor being reflected but just can't move anymore when coming to a playfield boundary.