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2. Vertex (geometry) - Wikipedia

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

   where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.

3. Vertex configuration - Wikipedia

   en.wikipedia.org/wiki/Vertex_configuration

   A vertex configuration can also be represented as a polygonal vertex figure showing the faces around the vertex. This vertex figure has a 3-dimensional structure since the faces are not in the same plane for polyhedra, but for vertex-uniform polyhedra all the neighboring vertices are in the same plane and so this plane projection can be used to visually represent the vertex configuration.

4. Two ears theorem - Wikipedia

   en.wikipedia.org/wiki/Two_ears_theorem

   The two vertices at the ends of the chain of triangles form ears. However, this polygon also has other ears that are not evident in this triangulation. In geometry, the two ears theorem states that every simple polygon with more than three vertices has at least two ears, vertices that can be removed from the polygon without introducing any ...

5. Vertex (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Vertex_(graph_theory)

   A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...

6. Vertex (curve) - Wikipedia

   en.wikipedia.org/wiki/Vertex_(curve)

   The dots are the vertices of the curve, each corresponding to a cusp on the evolute. In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. [1] This is typically a local maximum or minimum of curvature, [2] and some authors define a vertex to be more specifically a local extremum of curvature. [3]

7. Pick's theorem - Wikipedia

   en.wikipedia.org/wiki/Pick's_theorem

   The subdivision of the polygon into triangles forms a planar graph, and Euler's formula + = gives an equation that applies to the number of vertices, edges, and faces of any planar graph. The vertices are just the grid points of the polygon; there are = + of them. The faces are the triangles of the subdivision, and the single region of the ...