Pex's tactics are said to be much sharper than those of Hex.

Freecivs graphics system is configurable: originally, map display was always in overhead mode ( like in Civ I ), which many players found rather crude ; isometric mode ( like in Civ II ) and optionally hexagonal tiling ( like in Civ V ) were added later.

The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled ; i. e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions.

In 1961, Hao Wang asked whether determining if a set of tiles admits a tiling of the plane is an algorithmically unsolvable problem or not.

Icosahedral quasicrystals in three dimensions were projected from a six-dimensional hypercubic lattice by Peter Kramer and Roberto Neri in 1984 .< ref > The tiling is formed by two tiles with rhombohedral shape.

In geometry a self-replicating tiling is a tiling pattern in which several congruent tiles may be joined together to form a larger tile that is similar to the original.

Pex is nearly identical to Hex, except that it's played on a rhombus-shaped tiling of irregular pentagons, instead of regular hexagons.

It is possible to choose many different sets of prototiles for a tiling: translating or rotating any one of the prototiles produces another valid set of prototiles.

A set of prototiles is said to be aperiodic if every tiling with those prototiles is an aperiodic tiling.

The three-dimensional Schmitt-Conway-Danzer tile is the prototile of a monohedral aperiodic tiling of three-dimensional Euclidean space, but it remains open whether there is a monohedral aperiodic prototile for the plane.

( This essentially simulates an infinite periodic tiling, and in the field of partial differential equations is sometimes referred to as periodic boundary conditions.

The tiling is designed by Chris Southern, who worked with Hundertwasser on the Kawakawa toilets.

In 1961, Wang conjectured that if a finite set of tiles can tile the plane, then there exists also a periodic tiling, i. e., a tiling that is invariant under translations by vectors in a 2-dimensional lattice, like a wallpaper pattern.

This is similar to a Penrose tiling, or the arrangement of atoms in a quasicrystal.

* Michael F. Cohen, Jonathan Shade, Stefan Hiller, Oliver Deussen ( 2003 ), Wang Tiles for Image and Texture Generation introduces stochastic tiling and is very popular.

Thus, for a substitution tiling the eigenvalues of the substitution matrix should be Pisot numbers.

Partition walls constructed from fibre cement sheeting are popular as bases for tiling in kitchens or in wet areas like bathrooms.

From the 9th century onwards the distinctive Islamic tradition of glazed and brightly coloured tiling for interior and exterior walls and domes developed.

In other cases, simply tiling the screen and binding each sprite into the tiles it overlaps provides sufficient pruning, and for pairwise checks, bounding rectangles or circles called hitboxes are used and deemed sufficiently accurate.

* Identical rhombi can tile the 2D plane in three different ways, including, for the 60 ° rhombus, the Rhombille tiling.

* The Chapelle Imperiale built for Empress Eugenie, which has an intricately decorated roof interior, and elegant wall tiling.

: The user can select bitmap images ( referred to as " textures ") for tiling interface backgrounds and button and tab faces, or simply disable this feature.

Artist Jim Power, known as the " Mosaic Man " for his public art tiling the neighborhood

: 3ds Max offers operations for creative texture and planar mapping, including tiling, mirroring, decals, angle, rotate, blur, UV stretching, and relaxation ; Remove Distortion ; Preserve UV ; and UV template image export.

Sets of overlapping clones that form a contiguous stretch of DNA are called contigs ; the minimum number of clones that form a contig that covers the entire chromosome comprise the tiling path that is used for sequencing.

The Library of Congress uses various large format digital scans for " American Memories " ( its website of old images and maps ) in the current JPEG 2000 format ( which allows quick small images, remote tiling, remote enlargement ), and the older MrSID, JPEG, and TIFF formats.

The platforms feature the green, blue, black and white tiling scheme first used for the reconstruction and extension to Morden of the City & South London Railway ( now the Northern Line ) also designed by Holden and opened between 1924 and 1926.

Historians consider the techniques and tools for tiling as well advanced, evidenced by the fine workmanship and close fit of the tiles.

Typical turquoise tiling becomes popular in 10th-11th century and is used mostly for Kufic inscriptions on mosque walls.

Thus the simplest examples are a triangular lattice with or without connecting lines, and a hexagonal tiling with one color for outlining the hexagons and one for the background.

* Example tiling for each group, with dynamic demos of properties

* Overview with example tiling for each group

Given a fundamental domain for the group action ( for the full, orientation-reversing symmetry group, a ( 2, 3, 7 ) triangle ), the reflection domains ( images of this domain under the group ) give a tiling of the quartic such that the automorphism group of the tiling equals the automorphism group of the surface – reflections in the lines of the tiling correspond to the reflections in the group ( reflections in the lines of a given fundamental triangle give a set of 3 generating reflections ).

By interpreting the upper half of the complex plane as a model of the hyperbolic plane ( the Poincaré half-plane model ) Ford circles can also be interpreted as a tiling of the hyperbolic plane by horocycles.

A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling.

If we take such a tiling and enlarge it so that the formerly smallest tile now has the size of the square S we started out from, then we see that we obtain from this a tiling of the plane with integral squares, each having a different size.

Typically a geodesic dome design begins with an icosahedron inscribed in a hypothetical sphere, tiling each triangular face with smaller triangles, then projecting the vertices of each tile to the sphere.

These rectangular bricks are connected in a tessellation which, considered as an edge-to-edge tiling, is topologically identical to a hexagonal tiling ; each hexagon is flattened into a rectangle whose long edges are divided in two by the neighboring bricks.

This basketweave tiling is topologically identical to the Cairo pentagonal tiling, with one side of each rectangle counted as two edges, divided by a vertex on the two neighboring rectangles.

If this parallelogram pattern is colored before tiling it over a plane, seven colors are required to ensure each complete parallelogram has a consistent color that is distinct from that of adjacent areas.

In black and white there are also 17 wallpaper groups ; e. g., a colored tiling is equivalent with one in black and white with the colors coded radially in a circularly symmetric " bar code " in the centre of mass of each tile.

A quotient of any tiling in the ( 2, 3, 7 ) family can be used ( and will have the same automorphism group ); of these, the two regular tilings are the tiling by 24 regular hyperbolic heptagons, each of degree 3 ( meeting at 56 vertices ), and the dual tiling by 56 equilateral triangles, each of degree 7 ( meeting at 24 vertices ).

Corresponding to each tiling of the quartic ( partition of the quartic variety into subsets ) is an abstract polyhedron, which abstracts from the geometry and only reflects the combinatorics of the tiling ( this is a general way of obtaining an abstract polytope from a tiling ) – the vertices, edges, and faces of the polyhedron are equal as sets to the vertices, edges, and faces of the tiling, with the same incidence relations, and the ( combinatorial ) automorphism group of the abstract polyhedron equals the ( geometric ) automorphism group of the quartic.