"surviving illuminated manuscripts were produced in the 13th century, about half in the last forty years of the Latin kingdom; to what extent this is an accident of survival is unclear. Another example of the mixture of styles is the Church of the Holy Sepulchre in Jerusalem, the renovation and rebuilding of which was completed in 1149; however only fragments of the large programme of mosaics now survive. A mosaic is a type of art that uses of glass shards, tiles or small pebbles in order to create a picture. Some icons in wall painting and mosaic survive from the"
"tessellation, made with more than one kind of regular polygon but still having the same arrangement of polygons at every corner. Irregular tessellations can also be made from other shapes such as pentagons, polyominoes and in fact almost any kind of geometric shape. The artist M. C. Escher is famous for making tessellations with irregular interlocking tiles, shaped like animals and other natural objects. If suitable contrasting colours are chosen for the tiles of differing shape, striking patterns are formed, and these can be used to decorate physical surfaces such as church floors. More formally, a tessellation or tiling is"
"Opus tessellatum Opus tessellatum is the Latin name for the normal technique of Greek and Roman mosaic, made from tesserae that are larger than about 4 mm. It is distinguished from the finer ""opus vermiculatum"" which used tiny ""tesserae"", typically cubes of 4 millimetres or less, and was produced in workshops in relatively small panels which were transported to the site glued to some temporary support. ""Opus tessellatum"" was used for larger areas and laid down at the final site. The two techniques were often combined, with small panels of ""opus vermiculatum"" called ""emblemata"" at the centre of a larger"
"Tessellated roof Tessellated roof is a frame and a self-supporting structural system in architecture. A simple ridged roof may inside be a tessellated system. The interlinking shapes are replicated across the moulded surface using curvilinear coordinates, a specific technique with rigid interlinking beams, having characteristics similar to woven fabric. A tessellated roof is one of the most flexible framed systems to design. The measurements and precision are complex and commonly part of a computer-aided design process of production. It is used in a honeycomb geometry form, in the biomes of the Eden Project. It can be fabricated to fit a"
"design in ""opus tessellatum"". The tiny ""tesserae"" of ""opus vermiculatum"" allowed very fine detail, and an approach to the illusionism of painting. There was a distinct native Italian style of ""opus tessellatum"" using only black on a white background, which was no doubt cheaper than fully coloured work. Opus tessellatum is usually used for backgrounds consisting of horizontally or vertically arranged lines — but not both in a grid, which would be ""opus regulatum"". Opus tessellatum Opus tessellatum is the Latin name for the normal technique of Greek and Roman mosaic, made from tesserae that are larger than about 4"
"supported entirely by the surrounding buildings. A tessellated roof can convert previous outdoor space into a dry public area; some examples of this method are Galleria Vittorio Emanuele II and many other shopping complexes or the Queen Elizabeth II Great Court at the British Museum in London by Norman Foster. Tessellated roof Tessellated roof is a frame and a self-supporting structural system in architecture. A simple ridged roof may inside be a tessellated system. The interlinking shapes are replicated across the moulded surface using curvilinear coordinates, a specific technique with rigid interlinking beams, having characteristics similar to woven fabric. A"
"car doors or drinks cans. Tessellation is apparent in the mudcrack-like cracking of thin films – with a degree of self-organisation being observed using micro and nanotechnologies. The honeycomb provides a well-known example of tessellation in nature with its hexagonal cells. In botany, the term ""tessellate"" describes a checkered pattern, for example on a flower petal, tree bark, or fruit. Flowers including the fritillary and some species of ""Colchicum"" are characteristically tessellate. Many patterns in nature are formed by cracks in sheets of materials. These patterns can be described by Gilbert tessellations, also known as random crack networks. The Gilbert"
"to make mosaics. The word ""tessella"" means ""small square"" (from ""tessera"", square, which in turn is from the Greek word τέσσερα for ""four""). It corresponds to the everyday term ""tiling"", which refers to applications of tessellations, often made of glazed clay. Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as ""tiles"", can be arranged to fill a plane without any gaps, according to a given set of rules. These rules can be varied. Common ones are that there must be no gaps between tiles, and that no corner of one"
"the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, 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. Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles. Decorative mosaic tilings made of small squared blocks called tesserae were widely employed in classical antiquity, sometimes displaying geometric patterns. In 1619 Johannes Kepler made an early documented study of"
"tessellation is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures. The model, named after Edgar Gilbert, allows cracks to form starting from randomly scattered over the plane; each crack propagates in two opposite directions along a line through the initiation point, its slope chosen at random, creating a tessellation of irregular convex polygons. Basaltic lava flows often display columnar jointing as a result of contraction forces causing cracks as the lava cools. The extensive crack networks that develop often produce hexagonal columns of lava. One example of such an array of columns is the Giant's"
"tessellations. He wrote about regular and semiregular tessellations in his ""Harmonices Mundi""; he was possibly the first to explore and to explain the hexagonal structures of honeycomb and snowflakes. Some two hundred years later in 1891, the Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries. Fyodorov's work marked the unofficial beginning of the mathematical study of tessellations. Other prominent contributors include Aleksei Shubnikov and Nikolai Belov (1964), and Heinrich Heesch and Otto Kienzle (1963). In Latin, ""tessella"" is a small cubical piece of clay, stone or glass used"
"group. These tessellations only represent four symmetry space groups, and also all within the cubic crystal system. Many of these tessellations can be defined in multiple symmetry groups, so in each case the highest symmetry is expressed. These four symmetry groups are labeled as: Architectonic and catoptric tessellation In geometry, John Horton Conway defines architectonic and catoptric tessellations as the uniform tessellations (or honeycombs) of Euclidean 3-space and their duals, as three-dimensional analogue of the Platonic, Archimedean, and Catalan tiling of the plane. The singular vertex figure of an architectonic tessellation is the dual of the cell of catoptric tessellation."
"a tessellated pattern of cartoon-like figures in oriental attire. Metamorphosis I Metamorphosis I is a woodcut print by the Dutch artist M. C. Escher which was first printed in May, 1937. This piece measures and is printed on two sheets. The concept of this work is to morph one image into a tessellated pattern, then gradually to alter the outlines of that pattern to become an altogether different image. From left to right, the image begins with a depiction of the coastal Italian town of Atrani (see ""Atrani, Coast of Amalfi""). The outlines of the architecture then morph to a"
"is called ""non-periodic"". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. In the geometry of higher dimensions, a space-filling or honeycomb is also called a ""tessellation of space"". A real physical tessellation is a tiling made of 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 geometric tiling of the Alhambra palace. In the twentieth century,"
"tessellated human and animal figures into his artworks. In a 1958 letter from Escher to H. S. M. Coxeter, Escher wrote that he was inspired to make his ""Circle Limit"" series by a figure in Coxeter's article ""Crystal Symmetry and its Generalizations"". Coxeter's figure depicts a tessellation of the hyperbolic plane by right triangles with angles of 30°, 45°, and 90°; triangles with these angles are possible in hyperbolic geometry but not in Euclidean geometry. This tessellation may be interpreted as depicting the lines of reflection and fundamental domains of the (6,4,2) triangle group. An elementary analysis of Coxeter's figure,"
"concentrations of surviving mosaic artworks. Approximately half of all surviving tessellated Greek mosaics from the Hellenistic period come from Delos. The paved walkways of Delos range from simple pebble or chip-pavement constructions to elaborate mosaic floors composed of tesserae. Most motifs contain simple geometric patterns, while only a handful utilize the ""opus tessellatum"" and ""opus vermiculatum"" techniques to create lucid, naturalistic, and richly colored scenes and figures. Mosaics have been found in places of worship, public buildings, and private homes, the latter usually containing either an irregular-shaped floor plan or peristyle central courtyard. Although there are minor traces of Punic-Phoenician"
"Architectonic and catoptric tessellation In geometry, John Horton Conway defines architectonic and catoptric tessellations as the uniform tessellations (or honeycombs) of Euclidean 3-space and their duals, as three-dimensional analogue of the Platonic, Archimedean, and Catalan tiling of the plane. The singular vertex figure of an architectonic tessellation is the dual of the cell of catoptric tessellation. The cubille is the only Platonic (regular) tessellation of 3-space, and is self-dual. There are other uniform honeycombs constructed as prismatic stacks (and their duals) which are excluded from these categories. The pairs of architectonic and catoptric tessellations are listed below with their symmetry"
"establishing the genre in the origami mainstream. Around the same time period, Ron Resch patented some tessellation patterns as part of his explorations into kinetic sculpture and developable surfaces, although his work was not known by the origami community until the 1980s. Chris Palmer is an artist who has extensively explored tessellations after seeing the Zilij patterns in the Alhambra, and has found ways to create detailed origami tessellations out of silk. Robert Lang and Alex Bateman are two designers who use computer programs to create origami tessellations. The first international convention devoted to origami tessellations was hosted in Brasília"
"The Romans distinguished between normal ""opus tessellatum"" with ""tesserae"" mostly over 4 mm across, which was laid down on site, and finer ""opus vermiculatum"" for small panels, which is thought to have been produced offsite in a workshop, and brought to the site as a finished panel. The latter was a Hellenistic genre which is found in Italy between about 100 BC and 100 AD. Most signed mosaics have Greek names, suggesting the artists remained mostly Greek, though probably often slaves trained up in workshops. The late 2nd century BC Nile mosaic of Palestrina is a very large example of"
"Tessellation A tessellation of a flat surface 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 and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern"
"tessellations by a generalization of the Schläfli symbol by Boris Delauney and Andreas Dress, by which any tessellation (of any dimension) may be represented by a finite structure, which we may call a Dress–Delaney symbol. Any effective enumerator of Dress–Delaney symbols can effectively enumerate those periodic nets that correspond to tessellations. The three-dimensional Dress–Delaney symbol enumerator of Delgado-Friedrichs ""et al."" has predicted several novel crystal nets that were later synthesized. Meanwhile, a two-dimensional Dress–Delaney enumerator generating reticulations of two-dimensional hyperbolic space that is surgically dissected and wrapped around a triply periodic minimal surface such as the Gyroid, Diamond or Primitive,"
"including Roman art historian Katherine Dunbabin, for relying on overly broad stylistic parallels between the works. Portions of the Zliten mosaic are realized through a combination of three techniques: opus tessellatum, opus vermiculatum and opus sectile. The external black and white geometric border is created with the opus tessellatum technique. The central part of the mosaic is composed of geometric alternating square panels with each side measuring and realized in the opus sectile technique. Within these panels are circular ""emblemata"" depicting fish and other marine creatures (shrimp, murex, picarel, conger, sea urchin, garfish etc...) in the opus vermiculatum technique. Zliten"
"from infinitely far away rise like rockets perpendicularly from the limit and are at last lost in it, ever reaches the boundary line."" Tessellated designs often appear on textiles, whether woven, stitched in or printed. Tessellation patterns have been used to design interlocking motifs of patch shapes in quilts. Tessellations are also a main genre in origami (paper folding), where pleats are used to connect molecules such as twist folds together in a repeating fashion. Tessellation is used in manufacturing industry to reduce the wastage of material (yield losses) such as sheet metal when cutting out shapes for objects like"
"Basse-taille Basse-taille (bahss-tah-ee) is an enamelling technique in which the artist creates a low-relief pattern in metal, usually silver or gold, by engraving or chasing. The entire pattern is created in such a way that its highest point is lower than the surrounding metal. A translucent enamel is then applied to the metal, allowing light to reflect from the relief and creating an artistic effect. It was used in the late Middle Ages, and then again in the 17th century. The technique had been known to the Ancient Romans, but was lost at the end of the Middle Ages until"
"artists who design innovative pieces of jewelry. Damascening Damascening is the art of inlaying different metals into one another—typically, gold or silver into a darkly oxidized steel background—to produce intricate patterns similar to niello. The English term comes from a perceived resemblance to the rich tapestry patterns of damask silk. The technique has a long history in Japan, where it was used to decorate katana fittings, particularly tsuba. Known as zougan(象嵌) in Japanese, it has developed its own subset of terms to describe the particular patterns, although ""shippou-zougan"" is an enamelling technique which most Westerners would consider closer to champlevé."
"Tessellation (computer graphics) In computer graphics, tessellation is used to manage datasets of polygons (sometimes called ""vertex sets"") presenting objects in a scene and divide them into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11. A key advantage of tessellation for realtime graphics is that it allows detail to be dynamically added and subtracted from a 3D polygon mesh and its silhouette edges based on control parameters (often camera distance). In previously leading realtime techniques such as parallax mapping and bump mapping, surface details could be simulated"
"Gemmail Gemmail (French, plural ""gemmaux"") describes a type of stained glass art developed during the 1930s by French painter Jean Crotti. Translated from French, the word literally means “enamel gem.” It differs from traditional stained glass techniques in that the individual pieces of colored glass are not joined by lead came, but overlapped and glued together with a clear substance. Pablo Picasso is said to have hailed gemmail as a new art form. Inside the Basilica of St. Pius X of Lourdes Bernadette Soubirous's Way of Light, based on sketches by René Margotton, depicts the eighteen apparitions together with scenes"
"was developed by John Smith in the 1970s to help inexperienced folders or those with limited motor skills. Some designers also like the challenge of creating within the very strict constraints. Origami tessellation is a branch that has grown in popularity after 2000. A tessellation is a collection of figures filling a plane with no gaps or overlaps. In origami tessellations, pleats are used to connect molecules such as twist folds together in a repeating fashion. During the 1960s, Shuzo Fujimoto was the first to explore twist fold tessellations in any systematic way, coming up with dozens of patterns and"
"Damascening Damascening is the art of inlaying different metals into one another—typically, gold or silver into a darkly oxidized steel background—to produce intricate patterns similar to niello. The English term comes from a perceived resemblance to the rich tapestry patterns of damask silk. The technique has a long history in Japan, where it was used to decorate katana fittings, particularly tsuba. Known as zougan(象嵌) in Japanese, it has developed its own subset of terms to describe the particular patterns, although ""shippou-zougan"" is an enamelling technique which most Westerners would consider closer to champlevé. Damascened-inlay jewelry, especially of Japanese origin, is"
"and preserved in the mid-3rd century after the city was destroyed by Persians. Mosaics are among the most enduring of Roman decorative arts, and are found on the surfaces of floors and other architectural features such as walls, vaulted ceilings, and columns. The most common form is the tessellated mosaic, formed from uniform pieces ""(tesserae)"" of materials such as stone and glass. Mosaics were usually crafted on site, but sometimes assembled and shipped as ready-made panels. A mosaic workshop was led by the master artist ""(pictor)"" who worked with two grades of assistants. Figurative mosaics share many themes with painting,"
"Theorem Stencil Theorem stencil, sometimes also called theorem painting or velvet painting, is the art of making stencils and using them to make drawings or paintings on fabric or paper. A vogue for theorem stencil painting began in England at the turn of the 18th century. The art was first taught to women in academies and boarding schools throughout colonial New England. It continued to be taught into the mid-1800s in many other areas. The designs are traditionally painted on velvet and the work is then framed or matted. The stencils are multiple overlays and designs are always three-dimensional, primitive"
"a cover of the Euclidean plane by a countable number of closed sets, called ""tiles"", such that the tiles intersect only on their boundaries. These tiles may be polygons or any other shapes. Many tessellations are formed from a finite number of prototiles in which all tiles in the tessellation are congruent to the given prototiles. If a geometric shape can be used as a prototile to create a tessellation, the shape is said to ""tessellate"" or to ""tile the plane"". The Conway criterion is a sufficient but not necessary set of rules for deciding if a given shape tiles"
"becoming increasingly impressionistic, taking advantage of the crystalline reflection of the tesserae, which was better suited to ""opus tessellatum"". It was eventually entirely abandoned for this style. Opus vermiculatum Opus vermiculatum is a method of laying mosaic tesserae to emphasise an outline around a subject. This can be of one or more rows and may also provide background contrast, eg as a shadow, sometimes with Opus tessellatum. The outline created is often light and offset by a dark background for greater contrast. The name ""opus vermiculatum"" literally means ""worm-like work"", and has been described as one of the most demanding"