Q: What kind of polygon can be used for tessellations?

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Tessellations of regular polygons can occur only when the external angle of a polygon is equal to a factor of 360. As such, the only tessellations of regular polygons can occur when the internal angles of a polygon are equal to a factor of 360. As such, the only regular polygons which tessellate are triangles, squares, and hexagons.

There are eight different types of semiregular tessellations. Also called Archimedean tessellations, they occur when two or more convex regular polygons form tessellations of the plane in a way each polygon vertex is surrounded by the same polygons and in the same order.

Sometimes. By definition, a semi-regular tessellation must include more than one type of regular polygon. Some uniform tessellations use more than one type of regular polygon, but many uniform tessellations use only a single regular polygon. Therefore the statement is only sometimes true.

It is a convex polygon.

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No. Regular tessellations use only one polygon. And, according to the strict definition of regular tessellation, the polygon must be regular. Then a tessellation using rectangles, for example, cannot be called regular.

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Tessellations of regular polygons can occur only when the external angle of a polygon is equal to a factor of 360. As such, the only tessellations of regular polygons can occur when the internal angles of a polygon are equal to a factor of 360. As such, the only regular polygons which tessellate are triangles, squares, and hexagons.

There are eight different types of semiregular tessellations. Also called Archimedean tessellations, they occur when two or more convex regular polygons form tessellations of the plane in a way each polygon vertex is surrounded by the same polygons and in the same order.

Regular tessellations can be made using triangles, squares, and hexagons.

Sometimes. By definition, a semi-regular tessellation must include more than one type of regular polygon. Some uniform tessellations use more than one type of regular polygon, but many uniform tessellations use only a single regular polygon. Therefore the statement is only sometimes true.

All tessellations, involve inlaying, its the materials used and the designs applied that make the difference.

Artists, designers, architects, and mathematicians are some occupations that use tessellations in their work. For artists and designers, tessellations can be used in creating patterns and designs. In architecture, tessellations can be utilized in developing tiling and paving designs. Mathematicians study the properties and characteristics of tessellations as part of geometry.

rotations and translations

A tessellation that uses more than one type of regular polygon in an isogonal arrangement is known as a emu-regular tessellation. There are eight semi-regular tessellations that can be described by their vertex configuration.Ê

Tessellations have been used in art and architecture since ancient times, with examples found in cultures such as Islamic art and Roman mosaics. However, the term "tessellation" was not used until the 17th century, popularized by mathematicians like Kepler and Escher.