A graph 
is called 
-polytopal if there exists a 
-dimensional convex polytope 
such that the vertices and edges of
are in a one-to-one
incidence-preserving correspondence with those of 
. In other words 
is 
-polytopal iff it is isomorphic to
the 1-skeleton of some convex 
-polytopes 
. If 
, the graph is called a polyhedral
graph.
Polytopal Graph
See also
Polyhedral GraphExplore with Wolfram|Alpha
References
Grünbaum, B. "Polytopal Graphs." In Studies in Graph Theory, Part 2 (Ed. D. R. Fulkerson). Washington, DC: Math. Assoc. Amer., pp. 201-224, 1975.Referenced on Wolfram|Alpha
Polytopal GraphCite this as:
Weisstein, Eric W. "Polytopal Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PolytopalGraph.html