[izvzckoo] pinwheel knight

consider a fairy chess piece that can make a subset of knight moves: starting from (0,0), it can jump to (1,2) (2,-1) (-1,-2) (-2,1).  the pattern of destinations looks like a pinwheel.

this piece is colorbound, but not among just the 2 colors of a checkerboard like the chess bishop.  instead, there are 5 colors.  an orthogonally aligned unit cell of colors is given below.

a b c d e
d e a b c
b c d e a
e a b c d
c d e a b

this is a latin square plus diagonals, so a compound of this piece with a ferz would make it no longer colorbound.  adding just one more knight move would also make it not colorbound: slopes of 1/2 or -2 in the unit cell tessellated hit all colors.  but adding pinwheel camel moves (3,1) (-1,3) (-3,-1) (1,-3) keeps it colorbound the same way.

this tessellation of colored squares can be constructed (in many ways) out of congruent pieces of area 5.  one construction, not requiring piece rotations, is a square centered at the origin with vertices (1.5,0.5) (-0.5,1.5) (-1.5,-0.5) (0.5,-1.5).  the edges of this area-5 square are parallel to the permitted pinwheel knight moves.  the edges cut through chessboard squares; when tessellated, the broken chessboard squares wrap around.