Chamfered Square Tiling on:
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/ref> With large squares it has been called a ''Dijon tile pattern''. As 3 rows of rectangles, it has been called a ''basketweave tiling'' and ''triple block tile pattern ''.Laying Patterns
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In geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the chamfered square tiling or semitruncated square tiling is a tiling of the Euclidean plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions ...
. It is a square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex.
Conway called it a quadrille.
The internal angle of th ...
with each edge chamfered
A chamfer or is a transitional edge between two faces of an object. Sometimes defined as a form of bevel, it is often created at a 45° angle between two adjoining right-angled faces.
Chamfers are frequently used in machining, carpentry, f ...
into new hexagonal faces.
It can also be seen as the intersection of two truncated square tiling
In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex. This is the only edge-to-edge tiling by regular convex polygons which contains an octagon ...
s with offset positions. And its appearance is similar to a truncated square tiling, except only half of the vertices have been truncated, leading to its descriptive name ''semitruncated square tiling''.
Usage and Names in tiling patterns
In floor tiling, this pattern with small squares has been labeled as ''Metro Broadway Matte'' and ''alternate corner square tile''.Tile Patterns Gallery/ref> With large squares it has been called a ''Dijon tile pattern''. As 3 rows of rectangles, it has been called a ''basketweave tiling'' and ''triple block tile pattern ''.
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Variations
Variations can be seen in different degrees of ''truncation''. As well, geometric variations exist within a given symmetry. The second row shows the tilings with a 45 degree rotation which also look a little different. Lower symmetry forms are related to the cairo pentagonal tiling with axial edges expanded into rectangles. The chiral forms be seen as two overlapping pythagorean tilings.Semikis square tiling
The dual tiling looks like a square tiling with half of the squares divided into central triangles. It can be called a semikis square tiling, as alternate squares with kis operator applied. It can be seen as 4 sets of parallel lines. :
References
{{commons category Euclidean tilings