In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles).〔(Weisstein, Eric W. "Square." From MathWorld--A Wolfram Web Resource. )〕 It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ''ABCD'' would be denoted .
The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.
A square has Schläfli symbol . A truncated square, t, is an octagon, . An alternated square, h, is a digon, .
A convex quadrilateral is a square if and only if it is any one of the following:〔Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, p. 59, ISBN 1-59311-695-0.〕〔(J. Wilson, ''Problem set 1.3'', 2010 )〕
* a rectangle with two adjacent equal sides
* a quadrilateral with four equal sides and four right angles
* a parallelogram with one right angle and two adjacent equal sides
* a rhombus with a right angle
* a rhombus with all angles equal
* a quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals
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