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Shift Tab

The Shift tab allows one to vary the spacing between tiles. With the default parameters, rectangular tiles are arranged so that their Geometric bounding boxes are touching. The following options are available to add or subtract space between the tiles:

Tiling dialog - Shift tab.
The Shift tab of the Tile Clones dialog.
A P1 symmetry tiling with a constant shift.
A P1 symmetry tiling with a constant shift of 10% (of the bounding box). There is an x shift for each column and a y shift for each row.
A P1 symmetry tiling with a constant shift 2.
A P1 symmetry tiling with a constant shift of 10% (of the bounding box). There is a y shift for each column and an x shift for each row.
A P1 symmetry tiling with a constant shift 3.
A P1 symmetry tiling with an exponential shift of 1.1 (2% shift in x and y).
A P1 symmetry tiling with a constant shift 4.
A P1 symmetry tiling with a random shift of 10% (of the bounding box) in both x and y.

Question: What is the symmetry of closely packed hexagons? The answer is P1 as can be seen below. One can use this fact to trivially generate the board for the game Hex invented independently by the mathematicians Piet Hein and John Nash.

A P1 symmetry tiling for closely packed hexagons.
Closely packed hexagons have a P1 symmetry tiling as shown on the left. On the right is the board for the game Hex. To generate both tilings, a hexagon was tiled using a shift in x of 50% and a shift in y of −25% per row.