Tessellation意思
Tessellation is a term used in geometry and mathematics, particularly in the field of tessellation theory, which is a branch of discrete geometry. It refers to the process of covering a plane with one or more shapes so that the shapes fit together perfectly without any gaps or overlaps, like tiles on a bathroom floor.
In a tessellation, the individual shapes are called tiles, and they can be polygons (such as triangles, squares, or hexagons) or more complex shapes. There are several types of tessellations, including:
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Regular Tessellations: These are formed by using one of the three regular polygons that can tile the plane: the equilateral triangle, the square, and the regular hexagon. Each of these polygons can be used alone to cover a plane without any gaps or overlaps.
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Semi-Regular Tessellations: These are formed by using two or more types of regular polygons that fit together in a repeating pattern without gaps or overlaps. For example, a pattern of squares and triangles can form a semi-regular tessellation.
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Uniform Tessellations: These are a special type of semi-regular tessellation that have certain properties, such as all vertices meeting at the same angle and all edges being the same length. There are only six types of uniform tessellations.
Tessellations are not limited to two-dimensional surfaces; they can also be applied to three-dimensional spaces, such as the surface of a sphere or the inside of a cube. In three dimensions, the process involves using polyhedra or other three-dimensional shapes to fill space without gaps or overlaps.
Tessellations have applications in a variety of fields, including architecture, art, and engineering, where they are used to create patterns and designs that can be repeated seamlessly.