...can be made in the physical world. Polyomino tiling problems ask whether copies of a single polyomino can tile (cover) a given region, such as a plane or a rectangle. In 1960’s Golomb [3] and Klarner =-=[4]-=- were the first to study these problems for 2 particular polyominoes. For the problem of rectangular tiling, extensive results have been found for certain polyominoes [5, 6]. Figure 4: Top row: all po...

...ded polyominoes can be made in the physical world. Polyomino tiling problems ask whether copies of a single polyomino can tile (cover) a given region, such as a plane or a rectangle. In 1960’s Golomb =-=[3]-=- and Klarner [4] were the first to study these problems for 2 particular polyominoes. For the problem of rectangular tiling, extensive results have been found for certain polyominoes [5, 6]. Figure 4:...

...ino-like objects made by attaching squares joined either at sides or corners (see Figure 4 top row). Note that polyplets are a subset of holey polyominoes. Another related idea is rounded polyominoes =-=[2]-=- (see Figure 4 bottom row). These are polyplets with rounded corners and bridges connecting diagonally adjacent squares. Unlike polyplets and holey polyominoes, rounded polyominoes can be made in the ...

...1960’s Golomb [3] and Klarner [4] were the first to study these problems for 2 particular polyominoes. For the problem of rectangular tiling, extensive results have been found for certain polyominoes =-=[5, 6]-=-. Figure 4: Top row: all polyplets of order 3. Bottom row: two rounded pentominoes with the same squares, but different connections (bridges). Image courtesy of http://www.ericharshbarger.org/pentomin...

...1960’s Golomb [3] and Klarner [4] were the first to study these problems for 2 particular polyominoes. For the problem of rectangular tiling, extensive results have been found for certain polyominoes =-=[5, 6]-=-. Figure 4: Top row: all polyplets of order 3. Bottom row: two rounded pentominoes with the same squares, but different connections (bridges). Image courtesy of http://www.ericharshbarger.org/pentomin...