Doctor Heinrich Heesch identified 28 different structures. Out of that
there are 9 general
tiles with the most complete line structures. All the
remaining 19 tiles are simplified forms
of the 9 general tiles.There is
rough grouping between the Heesch tile structure and the
17 wallpaper
groups.
(1) Tile No. 2 is TTTTTT, this tile has no rotation or glide mirror lines.
The wallpaper equivalent is
"p1" .
(2) Tile No. 7 is TCCTCC, the smallest rotation angle is half turn.
The wallpaper equivalent is
"p2" .
(3) Tile No. 9 is C3C3C3C3C3C3, the smallest rotation angle is 1/3 turn.
The wallpaper equivalent is
"p3" .
(4) Tile No. 13 is CC3C3C6C6, the smallest rotation angle is 1/6 turn.
The wallpaper equivalent is
"p6" .
(5) Tile No. 16 is CC4C4C4C4, the smallest rotation angle is 1/4 turn.
The wallpaper equivalent is
"p4" .
(6) Tile No. 18 is TG1G1TG2G2, with 2 pairs of glide mirror lines and no rotation.
Each of glide mirror pair is contigurous.
Since the glide lines are both vertical, this is similar to wallpaper
"pg"for one direction mirror.
(7) Tile No. 20 is TG1G2TG2G1, with 2 pairs of glide mirror lines and no
rotation.
Each glide mirror pair is interspersed.
Since the glide lines are both vertical, this is similar to
wallpaper "pg" for one direction mirror.
(8) Tile No. 24 is TCCTGG, with combination of T line, half-turn rotation and
glide mirror pair.
Since there is rotation with mirror, this
is similar to wallpaper "pgg" for double glide.
(9) Tile No. 28 is CG1CG2G1G2 with vertical and horizontal glide lines.
Since there is rotation and the 2 glide axes are perpendicular, this is similar to wallpaper "pgg" .
The 9 tiles above were implemented in
computer programs.
The programs allow mathematical rules to be enforced so that
all creative sketching will tile the plane with no gaps.
Computer generated
Escher tiles by William Chow 1979
Use of tessellations in art and product design 1980