A polyking is a set of squares in the square grid,
joined edge to edge or corner to corner.
It differs from a polyomino,
whose cells must be joined edge to edge.
there is only one monoking, the monomino.
There are two dikings:
To integrate a polyking is to arrange copies of it without
overlapping to form a polyomino.
Here I show minimal known integrations of polykings.
The solutions shown are not necessarily uniquely minimal.
Not every polyking can be integrated.
The smallest that cannot are octakings.
Here are some examples:
Where several solutions for a polyking have the same number of tiles,
I prefer one whose tiles do not cross.
At most 2 tiles are needed to integrate any pentaking.
There are 524 hexakings, too many to show here.
Instead I show only hexakings of which 3 or more copies are needed.
Last revised 2022-05-08.
Back to Polyform Exclusion,
Equalization, Variegation, and Integration
Col. George Sicherman