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A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
The snub square tiling is an Archimedean tiling, and as the dual to an Archimedean tiling this form of the Cairo pentagonal tiling is a Catalan tiling or Laves tiling. [14] It is one of two monohedral pentagonal tilings that, when the tiles have unit area, minimizes the perimeter of the tiles.
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.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360
One variations on this pattern, often called a Mediterranean pattern, is shown in stone tiles with smaller squares and diagonally aligned with the borders. Other variations stretch the squares or octagons. The Pythagorean tiling alternates large and small squares, and may be seen as topologically identical to the truncated square tiling. The ...
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms, 7 which are topologically distinct. (The truncated triangular tiling is topologically identical to the hexagonal tiling.)
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A labyrinth can be generated by tiles in the form of a white square with a black diagonal. As with the quarter-circle tiles, each such tile has two orientations. [3] The connectivity of the resulting labyrinth can be analyzed mathematically using percolation theory as bond percolation at the critical point of a diagonally-oriented grid.
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