The term "nonahedral graph" is used for a polyhedral 9-vertex graph by Gayathri (2018, p. 50). The corresponding enneahedra have 9 faces and are related to these graphs through duality. Daoud (2020) explicitly defines the term by nine vertices. Daoud and Saleh (2020) use a nine-face description in their abstract but a nine-vertex description in their conclusion.
Nonahedral Graph
See also
Enneahedron, Polyhedral 9-Vertex Graph, Polyhedral GraphExplore with Wolfram|Alpha
References
Daoud, S. N. "Number of Spanning Trees in the Sequence of Some Nonahedral Graphs." Util. Math. 115, 39-56, 2020. https://utilitasmathematica.com/index.php/Index/article/view/1498.Daoud, S. N. and Saleh, W. "Complexity Trees of the Sequence of Some Nonahedral Graphs Generated by Triangle." Heliyon 6, e04786, 2020. https://doi.org/10.1016/j.heliyon.2020.e04786.Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput. 37, 523-532, 1981. https://doi.org/10.1090/S0025-5718-1981-0628713-3.Gayathri, A. "A Study on Higher Order Triangular Sum Numbers of Polyhedral and Graceful Graphs." Math. Sci. Internat. Res. J. 7, 48-55, 2018. https://kanchiuniv.ac.in/wp-content/uploads/2022/02/Research-Compendium-2018.pdf.Referenced on Wolfram|Alpha
Nonahedral GraphCite this as:
Weisstein, Eric W. "Nonahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonahedralGraph.html