Square  

A square is a regular quadrilateral. 

Edges and vertices  4 
Schläfli symbol  {4} 
Coxeter–Dynkin diagrams  
Symmetry group  Dihedral (D_{4}) 
Area (with t=edge length) 
t^{2} 
Internal angle (degrees) 
90° 
Properties  convex, cyclic, equilateral, isogonal, isotoxal 
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles (90 degree angles, or right angles). A square with vertices ABCD would be denoted ABCD.
Contents 
The perimeter of a square whose sides have length t is
and the area is
In classical times, the second power was described in terms of the area of a square, as in the above formula. This led to the use of the term square to mean raising to the second power.
The coordinates for the vertices of a square centered at the origin and with side length 2 are (±1, ±1), while the interior of the same consists of all points (x_{0}, x_{1}) with −1 < x_{i} < 1.
The equation max(x^{2},y^{2}) = 1 describes a square. This means "x^{2} or y^{2}, whichever is larger, equals 1." The circumradius of this square is .
A square is both a rhombus (equal sides) and a rectangle (equal angles) and therefore has all the properties of both these shapes, namely:
In noneuclidean geometry, squares are more generally polygons with 4 equal sides and equal angles.
In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle.
In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger squares have smaller angles.
Examples:
Six squares can tile the sphere with 3 squares around each vertex and 120 degree internal angles. This is called a spherical cube. The Schläfli symbol is {4,3}. 
Squares can tile the Euclidean plane with 4 around each vertex, with each square having an internal angle of 90 degrees. The Schläfli symbol is {4,4}. 
Squares can tile the hyperbolic plane with 5 around each vertex, with each square having 72 degree internal angles. The Schläfli symbol is {4,5}. 

[[File:rightthumbA square and its diagonals.]]
A square is a shape with four equal sides and four corners that are all right angles (90 degrees). The diagonals of a square also cross at right angles. The angle between any diagonal and a side of a square is 45 degrees. A square has rotational symmetry of four. It has four lines of regular symmetry.
A square is a type of rectangle with all sides of equal length.
