Features of a Trigonal Board

The Step

The basic move is a single step to an adjacent cell. The step may be made across a side or edge or through a corner point or apex. The number of adjacent cells is a function of the angle subtended at the juncture of two cell sides.

Cell Shape Angle Adjacent Cells
Trig 60 12
Square 90 8
Hex 120 6

The step may be classified in two distinct ways:

  • by using the colour of the step's from and to cells - chromatic typing
  • by using the connection between the from and to cells - connective typing

There are two Chromatic types:
one where the cell colour changes, an allochromatic step (a-step); the other where the cell colour remains the same, an idiochromatic step (i-step).

There are also two Connective types:
one where the cells are connected at a point or apex, a pointwise or apical step (p-step); the other where the connection is along a line or edge, an edgewise or lineal step (e-step).

On a square based board p-steps are always i-steps and vice versa, and e-steps are always a-steps and vice versa. These identities are NOT true for the trig based board.

Diagram 1. illustrates this single step. From the red trig the blue trigs can be reached by an a-step, while the yellow trigs are reached by an i-step.

The Slide

This may be defined as

a series of steps of the same type all made in the same direction

and the direction of movement defined as

along a straight line drawn from the centre of the starting cell and passing through the adjacent cell that forms the first step of the slide.

Diagram 2. shows these directions: Red lines where the connection between immediately adjacent trigs alternates between edge and point (an alternating direction); Green lines where the connection is always an edge (a constant direction).

Examples of cells reachable by slides are shown in Diagram 3. Blue cells where the slide consists of a-steps in an alternating direction; Yellow where i-steps in a constant direction.

Knight's Move

This may be defined in 3 ways as

1. an a-step followed by an i-step continuing away from the starting cell; or

2. an e-step followed by a p-step continuing away from the starting cell; or

3. a p-step followed by an e-step continuing away from the starting cell

On a trig based board the order of chromatic steps is not significant, while with connective steps it is. On a square based board all 3 definitions lead to the same pattern.

The 3 variations of the knight's move are illustrated by Diagrams 4, 5 and 6 .

Diagram 6 shows the pattern referred to by Joe Joyce in
this comment for a piece termed a short knight.

Piece's and their pattterns off movement are discussed further here.

It should be noted that the number of cells reached by a knight's move decreases as the number of cell sides increases: 12 for trigs; 8 for squares; 0 for hexes. The hex board suffers from the fact that no i-steps are possible with the definition of adjacent given above. This is usually remedied by an extension to the definition of adjacent.

Adjacent Extension

The hexagonal board extension may be stated as follows:

Also considered as adjacent are those cells that are adjacent to two ordinarily adjacent cells that are themselves mutually adjacent, such that the same step-type exists between each pairing of the three cells

This extension adds no more cells when applied to squares, but adds 12 more cells when applied to trigs.

Diagram 7. shows the 6 extended a-step adjacent cells in a darker blue, while the 6 i-step ones are shown in orange. With the normally adjacent cells 3 are reached by e-steps and 9 by p-steps: with the extended adjacent cells 9 are reached by e-steps and 3 by p-steps.


With its ability to define steps in 2 unique ways and with a possible 24 cells capable of being considered adjacent the somewhat neglected trigonal board has much to offer the CV game designer.

Diagram 1.


Diagram 2.


Diagram 3.


Diagram 4.


Diagram 5.


Diagram 6.


Diagram 7.


Add a New Comment
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Share Alike 2.5 License.