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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.
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In geometry , a vertex in plural form: vertices or vertexes is a point where two or more curves , lines , or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect cross , or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place. A vertex is a corner point of a polygon , polyhedron , or other higher-dimensional polytope , formed by the intersection of edges , faces or facets of the object. Polytope vertices are related to vertices of graphs , in that the 1-skeleton of a polytope is a graph, the vertices of which correspond to the vertices of the polytope,  and in that a graph can be viewed as a 1-dimensional simplicial complex the vertices of which are the graph's vertices. However, in graph theory, vertices may have fewer than two incident edges, which is usually not allowed for geometric vertices. There is also a connection between geometric vertices and the vertices of a curve , its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve there will be a point of extreme curvature near each polygon vertex. A vertex of a plane tiling or tessellation is a point where three or more tiles meet;  generally, but not always, the tiles of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles.