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    Polyhedral Graph

    Alternate name

    c-net

    Basic definition

    A polyhedral graph is a network made up of the vertices and edges of a polyhedron. Polyhedral graphs are always planar.

    Detailed definition

    An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of a sphere by a 3-connected planar graph. Conversely, by a theorem of Steinitz as restated by Grünbaum, every 3-connected planar graph can be realized as a convex polyhedron. Polyhedral graphs are sometimes simply known as

    Related terms

    convex polyhedron | cubical graph | dodecahedral graph | icosahedral graph | k-connected graph | octahedral graph | planar connected graph | planar graph | Platonic graph | polyhedral formula | polyhedral group | polytopal graph | Schlegel graph | simple graph | skeleton | tetrahedral graph | Tutte's wheel theorem

    Educational grade level

    college level

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