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  2. Vertex (geometry) - Wikipedia

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

    In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. 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.

  3. 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 ...

  4. Sierpiński triangle - Wikipedia

    en.wikipedia.org/wiki/Sierpiński_triangle

    A level-5 approximation to a Sierpiński triangle obtained by shading the first 2 5 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise If one takes Pascal's triangle with 2 n {\displaystyle 2^{n}} rows and colors the even numbers white, and the odd numbers black, the result is an approximation to ...

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    (A degenerate triangle, whose vertices are collinear, has internal angles of 0° and 180°; whether such a shape counts as a triangle is a matter of convention. [ citation needed ] ) The conditions for three angles α {\displaystyle \alpha } , β {\displaystyle \beta } , and γ {\displaystyle \gamma } , each of them between 0° and 180°, to be ...

  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 ...

  7. Geodesic polyhedron - Wikipedia

    en.wikipedia.org/wiki/Geodesic_polyhedron

    All vertices are valence-6 except the 12 centered at the original vertices which are valence 5 A geodesic polyhedron is a convex polyhedron made from triangles . They usually have icosahedral symmetry , such that they have 6 triangles at a vertex , except 12 vertices which have 5 triangles.

  8. Regular graph - Wikipedia

    en.wikipedia.org/wiki/Regular_graph

    In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]

  9. Neighbourhood (graph theory) - Wikipedia

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

    The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v. The neighbourhood is often denoted ⁠ ⁠ or (when the graph is unambiguous) ⁠ ⁠. The same neighbourhood notation may also be used ...

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