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# Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. 

## Branko Grünbaum

Branko Grünbaum (ברנקו גרונבאום; born 2 October 1929) is a Yugoslavian-born mathematician and a professor emeritus at the University of Washington in Seattle.

## Checkerboard

A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which English draughts (checkers) is played.

## Circle packing

In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that all circles touch one another.

## Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

## Euclidean tilings by convex regular polygons

Euclidean plane tilings by convex regular polygons have been widely used since antiquity.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

## Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

## Internal and external angles

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

## Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

## Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

## Kissing number problem

In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.

## Kite (geometry)

In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

## List of convex uniform tilings

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.

## List of regular polytopes and compounds

This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

## Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

## Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

## Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

## Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

## Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

## Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane.

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

## Square lattice

In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.

## Trapezoid

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America.

## Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

## Truncated square tiling

In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex.

## Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

## Uniform coloring

In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive.

## Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## References

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