There are 8 tiles in with the short diagonal c2 elements are colocated and the c4 elements are also colocated.
One of the tiles is "compact" (without voids); the remaining seven have voids, and when the weight function is plotted show a ribbon (in green) where only have the corresponding area of the plane is covered by the tile.
Two copies can (obviously) be put together to tile a symmetric tile. The images below show one copy in red, and a copy rotated 180° in blue; the overlapping areas (the ribbons) are shown in magenta.
© 2015 Stewart R. Hinsley