Cylindrical pieces are those that play as if the board was a cylinder, successfully warping around the right and left edges. Here's an overview of the these pieces (In no specific order):
Cylindrical Knight:

Its new powers are only apparent when he's at the right, or left edges of the board, and its advantage is that it doesn't lose half of it's mobility, like the normal knight (Here, the knight can also move to the blue circles.)
Cylindrical Bishop:

Its value is enhanced because now it's as if it was always on a long diagonal, but now it also controls its diagonals properly (by having access to the half of the board it normally wouldn't.)
Cylindrical Rook:

Here, the King does no longer block the rook as it can warp to the other side.
Cylindrical Queen:

I wonder if this piece is too strong as to be unusable (because the game may become CQueen centric.)
Cylindrical "King":

If this king is too hard to mate maybe it shouldn't be a royal piece.
Cylindrical Pawn:

The new ability is only when it's around the edge, and only for capturing. This should remove it's pawn edge weakness. In this case, each pawn is attacking each other.
I guess that learning this variant may be easier for someone that has not played chess, because being used to normal chess, I kept overlooking most moves from these pieces.
I don't think these pieces are very popular, but I'd want to know if there's an easy way to figure out their values.

