Tiling with rectangles

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A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of 1 × 2 side ratio. The tilings with straight polyominoes of shapes such as 1 × 3, 1 × 4 and tilings with polyominoes of shapes such as 2 × 3 fall also into this category.

Congruent rectangles[edit]

Some tiling of rectangles include:

Stacked bond.png
Stacked bond
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Running bond
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Basket weave
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Basket weave
Herringbone bond.svg
Herringbone pattern

Tilings with non-congruent rectangles[edit]

The smallest square that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles.[1]


The smallest rectangle that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles.[1]

See also[edit]

Notes[edit]

  1. ^ a b Madachy, Joseph S (Winter 1996). "Problems and conjectures". Journal of Recreational Mathematics. 28 (1): 64. ISSN 0022-412X.