Vertex (geometry)

The corner, and the vertex in the geometry is a very excellent point of the boundary line or surface of an area.

The corners of the two-dimensional polygons ( polygons ) are the points at which the lines delimiting the sides meet. In the case of three-dimensional polyhedron ( polyhedron ) is defined as the points where (at least) three of the bounding surfaces meet, as corners. The corners of polyhedra are endpoints of edges.

In the case of a convex n-dimensional Polytopes a corner is characterized by the fact that she can not be represented as a real convex combination of two different points of Polytopes ( extremal ).

For three-dimensional polyhedron there is an equation that describes a relationship between the corners, edges and faces of an arbitrary convex polyhedron, the Eulerian Polyedersatz.

A regular dodecahedron has 12 faces ( hence its name ), 20 vertices and 30 edges.

A nonconvex polyhedra.

A nonconvex polyhedron with 12 vertices, 36 edges and 32 faces for which the Euler Polyedersatz does not apply.