# Foam-like graphs

What's the "official" name of a connected planar graph consisting entirely of polygons (cycles), glued together at edges, e.g. - among other things - without "end vertices" (of degree 1) and without edges not belonging to an inner face. Maybe something like "planar foam graph"?

Has this concept been generalized to higher dimensions: "3D foam graphs" (entirely consisting of polyhedrons, glued together at faces) and so on?

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I mean the outer face that you mean: the one that always exists when you draw a (finite) planar graph in the plane. And I wanted to exclude planar graphs like "two triangles connected by an edge" - the latter (edge) would not belong to an inner face. –  Hans Stricker Aug 23 '12 at 17:35

@HansStricker: You are right. By Steinitz Theorem every planar 3-connected graph can be realized as convex 3d polytope. Take any face $f$ and project all other vertices on $f$ (centrally to a vertex just behind $f$). In this way you get a Schlegel diagramm, which is a crossing free drawing of the graph, with $f$ as outer face, and all faces drawn as convex polygons. –  A.Schulz Aug 23 '12 at 19:58