Some tiles associated with the 6th unit cubic Pisot number

Order 7 Demisymmetric Tiles (4c2+c3+2c4)

III. long diagonal c2 and c4 elements merged

There are 8 tiles in with the long diagonal c1 elements are colocated and the c4 elements are also colocated.

order 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tile

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.

order 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric 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.

order 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tileorder 7 demisymmetric tile

© 2015 Stewart R. Hinsley