There was an unclosed B tag near the end of the page. I have now removed it.
Aside from that, I'm wondering if there's any disadvantage to rotational symmetry compared with mirror symmetry. Does it encourage symmetric positions more? It seems less popular for some reason.
Rotational symmetry is less popular, because Chess has mirror symmetry, and most Chess variants copy this feature of Chess. This mass copying of Chess should not imply that mirror symmetry is inherently better. Shogi has rotational symmetry and doesn't seem to be the worse for it.
One difference between Chess and Shogi is that Chess has a Queen beside the King. With mirror symmetry, Queens start in the same file, and moving a Pawn from the King's file has less chance of exposing the King to check. In Shogi, Kings both start in the center file, and rotational symmetry mainly affects the positions of Rook and Bishop, which are toward the sides. The rotational symmetry allows an early exchange of Bishops and keeps Rooks from engaging with each other until later in the game. So I would say that whether mirror or rotational symmetry is better will depend upon what pieces are in the game, where they are placed, and the dimensions of the game. So I don't think there is any hard and fast rule that one is always better in any Chess variant.
There was an unclosed B tag near the end of the page. I have now removed it.
Rotational symmetry is less popular, because Chess has mirror symmetry, and most Chess variants copy this feature of Chess. This mass copying of Chess should not imply that mirror symmetry is inherently better. Shogi has rotational symmetry and doesn't seem to be the worse for it.
One difference between Chess and Shogi is that Chess has a Queen beside the King. With mirror symmetry, Queens start in the same file, and moving a Pawn from the King's file has less chance of exposing the King to check. In Shogi, Kings both start in the center file, and rotational symmetry mainly affects the positions of Rook and Bishop, which are toward the sides. The rotational symmetry allows an early exchange of Bishops and keeps Rooks from engaging with each other until later in the game. So I would say that whether mirror or rotational symmetry is better will depend upon what pieces are in the game, where they are placed, and the dimensions of the game. So I don't think there is any hard and fast rule that one is always better in any Chess variant.