Four Decorated Tiles

thingiverse

Four square tiles 9 cm on a side, approximately the size of standard kitchen tiles. They are made from polyominos, two sets of 4 identical heptominos and a set of 4 identical hexominos, 80 squares in all, covering a 9x9 array of squares, the central square separately covered. The surfaces of the polyominos are marked with squares, hexagons, or sets of circles, so as distinguish them and show the symmetry of the arrangements. In the image above the two sets of heptominos are colored blue and green, and the set of hexominos is red. Four of the symmetries of the two dimensional point groups are shown by the tiles: P2mm, P4mm, P2 and P4. Mirror lines, m, are shown as white lines. Two and four fold rotation axis are perpindicular to the tile and pass through the center of the central square which is marked with a white x. The tiles can be backed with a sheet of cork to serve as coasters. OpenSCAD code is included. It contains a summary of the construction of the tiles and additional examples.