LOLWUT?

Since January 31, 2008

For each of those figures, a vertex is a point formed by the intersection of faces of the object: a vertex of a polygon is the point of intersection of two polygon edges, a vertex of a polyhedron is the point of intersection of three or more polyhedron facets, and a vertex of a d-dimensional polytope is the intersection point of d or more polytope facets. A vertex can also refer to an angle, the point where two rays begin or meet, where two line segments join or meet, where two lines cross (intersect), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.

In a polygon, a vertex is called "convex" if the internal angle of the polygon, that is, the angle formed by the two edges at the vertex, with the polygon inside the angle, is less than π radians; otherwise, it is called "concave" or "reflex". More generally, a vertex of a polyhedron or polytope is convex if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and concave otherwise.

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