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Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.
The order n>=2 L-polyomino consists of a vertical line of n squares with a single additional square attached at the bottom.
The unique 1-polyomino, consisting of a single square.
An octomino is an 8-polyomino. There are 369 free (illustrated above), 704 one-sided, and 2725 fixed octominoes.
The 4-polyhex illustrated above.
A polybe is a polyform formed from a polycubes by removing of half of each cube such that at least half of the original join between cubes is retained. The numbers of polybes ...
Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...
The term "polyedge" has been variously proposed to refer to a polystick or a simple connected graph on n edges (Muñiz 2011), the latter of which has also been termed an ...
Polypons are polyforms obtained from dividing a regular triangular grid into 30-30-120 triangles, illustrated above. The numbers of polypons with n=1, 2, ... components are ...
Polyrects are polyforms obtained from a rectangular grid, illustrated above. The numbers of polyrects with n=1, 2, ... components are 1, 2, 3, 9, 21, 68, 208, ... (OEIS ...
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