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www.quora.com/What-are-vertices-How-many-vertices-does-a...

Vertex is just a point. It can be just a single point without any edges also (Isolated vertices). And you can implement a graph that looks like square with any 4n number of vertices making sure the last vertex is connected to the first vertex and all egdes of unit length.

mathopenref.com/vertex.html

Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices. (Pronounced: "ver - tiss- ease"). A square for example has four vertices.

www.purplemath.com/modules/sqrvertx.htm

The vertex form of a quadratic is given by y = a(x – h) 2 + k, where (h, k) is the vertex. The "a" in the vertex form is the same "a" as in y = ax 2 + bx + c (that is, both a's have exactly the same value). The sign on "a" tells you whether the quadratic opens up or opens down.

www.reference.com/math/many-vertices-square-436e4c31f9ff972b

A square is a polygon with four vertices. The shape has four equal sides and four 90-degree angles; thus, it is called a regular quadrilateral. The sides meet in four corners, which are called vertices. A vertex is defined in geometry as the common endpoint of two or more rays or line segments.

A square is a plane (flat) shape whose boundaries are four straight lines of equal length such that these lines meet, in pairs, at four points (vertices).

If the square is sliding along a straight line then the path of the vertex is a straight line. If the square is rotating, the answer will vary according to the location of the centre of rotation.

en.wikipedia.org/wiki/Square_(geometry)

A crossed square is a faceting of the square, a self-intersecting polygon created by removing two opposite edges of a square and reconnecting by its two diagonals. It has half the symmetry of the square, Dih 2, order 4. It has the same vertex arrangement as the square, and is vertex-transitive.

math.stackexchange.com/questions/738973/finding-the-fourth...

Without drawing a graph and given the following 3 vertices, find the coordinates of the last vertex of the square: $(3,2)$$(0,5)$$(-3,2)$ So first, I found the length of the sides and the diagonal of the square, which are $\sqrt{18}$ and $6$ respectively. By graphing, I know the solution is $(0, -1)$.