FIDE Pieces for Trigonal Boards

Diagram 1 - 128 trig board

Diagram 2 a-step Wazir	Diagram 3 e-step Wazir
Diagram 4 i-step Ferz	Diagram 5 p-step Ferz
Diagram 6 Guard move	Diagram 7 Crusader
Diagram 8 Knight-Errant	Diagram 9 Paladin
Diagram 10 Victor	Diagram 11 Companion
Diagram 12 Dart
Diagram 13 Abbot	Diagram 14 Gyrkin
Diagram 15 Druid	Diagram 16 Sidewinder
Diagram 17 Turret
Diagram 18 Tower	Diagram 19 Dome
Diagram 20 Spire	Diagram 21 Belfry

Introduction

With its dual classification of steps and the availability of up to 12 ordinarily adjacent cells and 12 extended adjacent cells, the Trigonal board offers a versatile arena for piece design.

This page looks at adapting the FIDE pieces and gives an estimate of their value on a 128 cell trigonal board (Diagram 1). See also Delta Chess

There are several companion pages dealing with non-FIDE pieces:

• Short Range
• Long Leapers
• Sliders and Riders

Special thanks must go to Joe Joyce for his insight and inspiration in opening up and developing this topic.

King (Guard)

The King's move is described as a single step in any direction and may also be termed a Guard's move.

On a square board this move can be broken down into an orthogonal step (a Wazir's move) and a diagonal step (a Ferz' move).

On a trigonal board we can further distinguish between a-step and e-step Wazir, and i-step and p-step Ferz.

There is also the choice to be made between keeping to the unextended (u-) adjacent trigs or allowing the use of the extended (x-) adjacent cells.

What were two components on a board with square cells are now eight on the trigonal board, and may be referred to as:

• ua-step
• xa-step
• ue-step
• xe-step
• ui-step
• xi-step
• up-step
• xp-step

Diagrams 2,3,4 and 5 illustrate these components for a piece standing on the red trig. Light blue trigs are the reachable unextended adjacent trigs, while dark blue are the reachable extended.

Diagrm 6 shows the full King's (Guard) move.

For the purposes of adapting the FIDE pieces and estimating their value, I shall ignore the extended adjacent cells. The King's move on a trigonal board is thus demonstrated by the light-blue trigs in Diagrm 6.

Knight

On a square-based board the Knight's move may be described as a Ferz' move followed by a Wazir's in the same general direction - or,equivalently, vice-versa.

On a trigonal board, ignoring the extended adjacent cells, this translates to :

1. a-step then i-step
2. i-step then a-step
3. e-step then p-step
4. p-step then e-step

1 and 2 are equivalent, leading to 3 basic types of knights and 2 natural combinations, namely

Movement	Classification	Name
a+i or i+a	Chromatic or ch-knight	Knight-Crusader (Crusader)
e+p	Edge or e-knight	Knight-Errant
p+e	Point or p-knight	Knight-Paladin (Paladin)
e+p and p+e	Connective or cv-knight	Knight-Victor (Victor)
e+p and p+e and (a+i or i+a)	Complete or co-knight	Knight-Companion (Companion)

See Diagrams 7, 8, 9, 10 and 11.

Notes

1. The Paladin was first described by Joe Joyce in this comment
2. Following Joe's suggestion, both the Knight-Errant and Paladin may be termed short knights (maximum cells attacked is 9) while the Companion might be termed a long knight (attacks a maximum of 18 cells).

Bishop

The Bishop makes a series of Ferz' moves.

These may be i-ferz or p-ferz and the connecting point may remain constant or alternate. The resulting path made by the series of steps may be straight or curved.

Movement	Classification	Name
xi-ferz	Constant Point Straight Path	Dart
p-ferz	Alternate Point Straight Path	Abbot
p-ferz	Constant Point Curved Path	Gyrkin
i-ferz or p-ferz	Constant Point Straight Path	Druid
i-ferz or p-ferz	Alternate Point Curved Path	Sidewinder

See Diagrams 12, 13, 14, 15 and 16.

Notes

1. The Dart is a slider, the slide consisting of a series of steps between extended adjacent trigs. Movement can only be blocked by pieces that occupy a trig that is part of the slide.
2. The Druid and the Sidewinder are colour-bound and are thus true trigonal analogues of the FIDE Bishop.
   The Abbot and the Gyrkin are not colour-bound and could equally well be placed in the list of Rooks. They might best be considered a third type of slider where the steps are both a-wazir and p-ferz: perhaps Chaplains might be a good term for this intermediate class of sliders?
3. Gyrkin is a falconry term for the male Gyrfalcon, a bird of prey that flies in circular patterns as it casts for quarry.

Rooks

The Rook makes a series of Wazir's moves.

These may be a-wazir or e-wazir and the connecting edge may remain constant or alternate. The resulting path made by the series of steps may be straight or curved.

Movement	Classification	Name
xa-wazir	Constant Edge Curved Path	Turret
a-wazir or e_wazir	Alternate Edge Straight Path	Tower
a-wazir or e-wazir	Constant Edge Curved Path	Dome
a-wazir	Constant Edge Straight Path	Spire
a-wazir	Alternate Edge/Point Curved Path	Belfry

See Diagrams 17, 18, 19, 20 and 21.

Notes

to be continued

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