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  2. Pick's theorem - Wikipedia

    en.wikipedia.org/wiki/Pick's_theorem

    [5] 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 ...

  3. 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.

  4. Vertex figure - Wikipedia

    en.wikipedia.org/wiki/Vertex_figure

    These are seen as the vertices of the vertex figure. Related to the vertex figure, an edge figure is the vertex figure of a vertex figure. [3] Edge figures are useful for expressing relations between the elements within regular and uniform polytopes. An edge figure will be a (n−2)-polytope, representing the arrangement of facets around a ...

  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. Hate crime suspect arrested, accused of assaulting ... - AOL

    www.aol.com/news/hate-crime-suspect-arrested...

    A man who is allegedly responsible for multiple assaults on transgender individuals within Atlanta, Georgia, has been arrested, police said. Michael Boykin, 28, was identified as a hate crime ...

  7. UFC star Colby Covington said he lost fight because he was ...

    www.aol.com/ufc-star-colby-covington-said...

    I came off the couch on two-and-a-half weeks notice. It’s a tough ending to go like that. I feel like I was just getting my wind and I was going to come out strong, but, you know, it is what it is."

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