Tessellation in the context of "Tile-based game"

The mosaics of Delos are a significant body of ancient Greek mosaic art. Most of the surviving mosaics from Delos, Greece, an island in the Cyclades, date to the last half of the 2nd century BC and early 1st century BC, during the Hellenistic period and beginning of the Roman period of Greece. Hellenistic mosaics were no longer produced after roughly 69 BC, due to warfare with the Kingdom of Pontus and the subsequently abrupt decline of the island's population and position as a major trading center. Among Hellenistic Greek archaeological sites, Delos contains one of the highest 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.

A unit of real estate or immovable property is limited by a legal boundary (sometimes also referred to as a property line, lot line or bounds). The boundary (in Latin: limes) may appear as a discontinuation in the terrain: a ditch, a bank, a hedge, a wall, or similar, but essentially, a legal boundary is a conceptual entity, a social construct, adjunct to the likewise abstract entity of property rights.

A cadastral map displays how boundaries subdivide land into units of ownership. However, the relations between society, owner, and land in any culture or jurisdiction are conceived of in terms more complex than a tessellation. Therefore, the society concerned has to specify the rules and means by which the boundary concept is materialized and located on the ground.

A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable and logical manner. There exists countless kinds of unclassified patterns, present in everyday nature, fashion, many artistic areas, as well as a connection with mathematics. A geometric pattern is a type of pattern formed of repeating geometric shapes and typically repeated like a wallpaper design.

Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world.

In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον  'arc') or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given two edges, there is a translation, rotation, and/or reflection that will move one edge to the other while leaving the region occupied by the object unchanged.

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.

Technically, one says that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope acts transitively on its vertices, or that the vertices lie within a single symmetry orbit.

In geometry, a tessellation of dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any two faces A and B, there must be a symmetry of the entire figure by translations, rotations, and/or reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.

Isohedral polyhedra are called isohedra. They can be described by their face configuration. An isohedron has an even number of faces.

A lozenge (/ˈlɒzɪndʒ/ LOZ-inj; symbol: ◊), often referred to as a diamond, is a form of rhombus. The definition of lozenge is not strictly fixed, and the word is sometimes used simply as a synonym (from Old French losenge) for rhombus. Most often, though, lozenge refers specifically to a thin rhombus, especially one with two acute angles of 45° and two obtuse angles of 135°.

The lozenge shape is often used in parquetry (with acute angles that are 360°/n with n being an integer higher than 4, because they can be used to form a set of tiles of the same shape and size, reusable to cover the plane in various geometric patterns as the result of a tiling process called tessellation in mathematics) and as decoration on ceramics, silverware and textiles. It also features in heraldry and playing cards.