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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.
Hopscotch pattern or Pythagorean tiling, a floor tile layout Topics referred to by the same term This disambiguation page lists articles associated with the title Hopscotch .
In the 1987 book, Tilings and patterns, Branko Grünbaum calls the vertex-uniform tilings Archimedean, in parallel to the Archimedean solids. Their dual tilings are called Laves tilings in honor of crystallographer Fritz Laves. [1] [2] They're also called Shubnikov–Laves tilings after Aleksei Shubnikov. [3]
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
In parquetry, more casually known as flooring, herringbone patterns can be accomplished in wood, brick, and tile.Subtle alternating colors may be used to create a distinctive floor pattern, or the materials used may be the same, causing the floor to look uniform from a distance.
Hopscotch is a popular playground game in which players toss a small object, called a lagger, [1] [2] into numbered triangles or a pattern of rectangles outlined on the ground and then hop or jump through the spaces and retrieve the object. [3] It is a children's game that can be played with several players or alone. [4]
Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings ...
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
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