Comments/Ratings for a Single Item

Interesting. I understand the idea. However several moves do not appear as "natural" for me. That notion of "naturally" is certainly very subjective and depends on who considers it.

The notation is not clear for me. I would recommend a void diagram on which each cell is identified with its coordinates.

The Rook is OK for me.

The Bishop is not. I am surprised to see the cells it may reach. Moreover I am not sure to understand which path it follows to reach these cells. I recommend to show the paths as well on the diagram.

The Knight is partly strange for me. OK for the 3 cells which are not on Rook's paths, they look natural for a Knight-equivalent. For the 6 others, they are like Dabbaba-equivalent. But, why not defining the Knight as such. OK.

I have a problem with the Bishop. As the matter of fact, this lies in how you define a diagonal for a triangle. That would deserve an explanation. You speak of diagonal but not all readers will catch it. Me, I confess I don't.

Don't take bad this feedback. Again, it's interesting.

@Jean-Louis Cazaux, that's an argumentative point, but I think you partially misunderstood me, due to my explanation and diagrams lacking enough clarity. The notation is simple - an odd number defines a line of dark cells, an even number defines white cells, etc. The columns are made of both white and dark cells except the very first. I didn't use numeral notation because it takes too much time to enter and place it on the diagram.

Bishop moves in a way similar to rook - it alternates between cells in an outer direction (meaning that it always should stay further from the starting point).

Instead of the rook with 6 directions, the bishop has 12. Red cells show a pattern like 'right-left-right-left' etc. For blue cells, it is reversed. From f6 you cannot move to e6 because it would violate the alternating pattern of both possible directions, and after reaching e5, everything continues from the initial perspective. Here's another take - if all dark cells will be converted to hexagons and combined together, the bishop's movement would look like a movement of an alternating hexagonal rook. It is the only way to achieve a constant movement without directions getting multiplied. A more clarifying diagram is added to cover all directions.

Knight's move is derivative of the rook's and bishop's move. You simply move the knight in any of three rook-alike directions, then in any bishop-alike, except g6, g8, and h8 for obvious reasons. The fact that it looks like the dabbaba's move purely lies on the board's geometry. I simply followed the principle borrowed from chess that after moving like a rook, it moves in a diagonal direction except for the cells placed directly to the starting cell.

Another formulation of the bishop's move:

1. Trigonal bishop is counted as an alternating hexagonal rook if the cells of the same color will be converted to vertical hexagons.
2. In this perspective, the bishop should move only forward, not sideways or otherwise.
3. And it should not move in a straight hexagonal rook-alike manner with more than two cells in a row to preserve the alternating pattern (for the rook it is a 'built-in' feature).

Why this way? a. The directions of the two sliding pieces are now opposite of each other, similar to chess; b both pieces use the same rule of movement; c since the bishop has 6 nearby 'diagonal' cells, unlike the rook with 3 orthogonal, it should have 12 directions of movement, not 6 like it was featured in other variants since rook already has 6. So, I think that the way the bishop moves is quite natural from the rook's perspective. The board is also naturally colored, and the pieces are arranged in a way similar to orthodox chess.

I feel that I may miss something, and I would be glad if someone could disprove this idea.

Some of the wording could be improved:

gliding piece -> sliding piece

outer side -> opposit/most distant side

angle -> corner

multiplying of their move -> branching of their trajectory

To me the Bishop's move doesn't look very natural either. The fact that after an even number of steps each destination can be reached through two paths makes it essentially different from a normal slider, and more like a 'crooked' piece. But of course you can make the pieces move as you want; there doesn't need to be a justification.

In the explanation of the coordinates it would help if you would label 3 or 4 of the cells with their coordinates. That will be enough to get the idea; there is no need to label all cells.

@H. G. Muller, the corrections were made.

To me the Bishop's move doesn't look very natural either. The fact that after an even number of steps each destination can be reached through two paths makes it essentially different from a normal slider, and more like a 'crooked' piece.

Sure, it's more like a kind of crooked piece, but the same thing goes with the rook, it simply looks like a straight path. It is the idea that was suggested, to make the rook and bishop work by the same rule.

But of course you can make the pieces move as you want; there doesn't need to be a justification.

Justification is the key element here, brought by this variant's idea. There's another way, which may suit the purpose better.

In the ideal condition for sliders, since the triangle has only three sides (and corners) and two of them are equal to each other in terms of trajectory selection, the branching of their directions should cover the whole board. That's what I also suggested with the only remark that the sliding pieces should always stay further from the initial cell and levels the piece already crossed, which can somewhat limit their power and make the game stable.

To contribute (hopefully clarifying, but at risk of doing the opposite) to the discussion of the pieces:

It is established that a triangular‐celled board is isomorphic to a hex‐cell board with one hex‐‘bishop’ binding inaccessible. On such a board, the usual triangular ‘rook’ — the same rook present here — becomes a crooked rook making 60° turns between steps (known to Gilman as a Longgirlhexer). The usual colourbound piece, moving in a straight line on triangles of the same colour to every second ‘rook’ cell is then equivalent to the hex ‘bishop’, while the usual ‘third’ rider, moving in a straight line alternating steps through the sides and across the corners, is a normal hex rook that can jump over the gaps (or, equivalently, a straight wazir–dabbaba alternator which I haven't seen named)

This game's bishop analogue is then equivalent to the crooked hex ‘bishop’ (Gilman's Longrangehexer), hence bearing the same relation to the rook analogue as the usual hex ‘bishop’ to the hex rook

The knight analogue here is equivalent to a hex dabbaba + hex ‘knight’; the pawn analogue is more unusual

@Bn Em, I think that I'm late to reply to this, but thank you for clarifying that.

John J. G. Savard, who runs quadibloc.com stated that pieces on triangular tiling 'naturally go around in circles' if direct 'hexagonal' logic will be applied as you described it; he also suggested that alternating movement can be seen as a solution, but no diagrams of it were provided although I believe that this idea can be executed similarly to mine. A one-direction movement which can be seen as an alternative to the alternating method doesn't work equally for both the rook and bishop. So, I think that my goal on this is completed.

I didn't know what to do with knight and pawn, so I simply followed the logic of orthodox chess.