Heesch Tiling

https://en.wikipedia.org/wiki/Heesch%27s_problem
In geometry, the Heesch number of a shape is the maximum number of layers of copies of the same shape that can surround it.
For example, a square may be surrounded by infinitely many layers of congruent squares in the square tiling, while a circle cannot be surrounded by even a single layer of congruent circles without leaving some gaps.
The Heesch number of the square is infinite and the Heesch number of the circle is zero. In more complicated examples a polygonal tile can be surrounded by several layers, but not by infinitely many; the maximum number of layers is the tile's Heesch number.