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The Laves tilings have vertices at the centers of the regular polygons, and edges connecting centers of regular polygons that share an edge. The tiles of the Laves tilings are called planigons. This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it.
There are one triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of rr{3,6}. John Conway calls it a rhombihexadeltille. [1] It can be considered a cantellated by Norman Johnson's terminology or an expanded hexagonal tiling by Alicia Boole Stott's operational language. There are three regular and eight semiregular ...
The smaller A-tile, denoted A S, is an obtuse Robinson triangle, while the larger A-tile, A L, is acute; in contrast, a smaller B-tile, denoted B S, is an acute Robinson triangle, while the larger B-tile, B L, is obtuse. Concretely, if A S has side lengths (1, 1, φ), then A L has side lengths (φ, φ, 1). B-tiles can be related to such A-tiles ...
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.
When it tiles the plane it will give a wallpaper group and when it tiles the sphere or hyperbolic plane it gives either a spherical symmetry group or Hyperbolic symmetry group. The type of space the polygons tile can be found by calculating the Euler characteristic , χ = V − E + F , where V is the number of corners (vertices), E is the ...
A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...