The term "heptahedral graph" is used for a polyhedral 7-vertex graph by Gayathri (2018, p. 50). The corresponding heptahedra have 7 faces and are related to these graphs through duality. Burgess et al. (2023, Sec. 3) use the name "heptahedral graph 34" for a particular seven-vertex member.
Heptahedral Graph
See also
Heptahedron, Polyhedral 7-Vertex Graph, Polyhedral GraphExplore with Wolfram|Alpha
References
Burgess, A. C.; Luther, R. D.; and Pike, D. A. "Existential Closure in Line Graphs." 4 Aug 2023. https://arxiv.org/abs/2211.01168v3.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
Heptahedral GraphCite this as:
Weisstein, Eric W. "Heptahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HeptahedralGraph.html