Tesselations
A tessellation is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions.Some special kinds of tessellations include regular, with tiles all of the same shape; semi-regular, with tiles of more than one shape; and aperiodic tilings, which use tiles that cannot form a repeating pattern. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups.In computer graphics, the term "tessellation" is used to describe the organization of information needed to render to give the appearance of the surfaces of realistic three-dimensional objects.In the real world, a tessellation is a tiling made of physical materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.
A tessellation is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions.Some special kinds of tessellations include regular, with tiles all of the same shape; semi-regular, with tiles of more than one shape; and aperiodic tilings, which use tiles that cannot form a repeating pattern. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups.In computer graphics, the term "tessellation" is used to describe the organization of information needed to render to give the appearance of the surfaces of realistic three-dimensional objects.In the real world, a tessellation is a tiling made of physical materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.
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