The term "hexahedral graph" is used for a polyhedral 6-vertex graph by Gayathri (2018, p. 50). The corresponding hexahedra have 6 faces and are related to these graphs through duality. The name is also used for the eight-vertex cubical graph, the skeleton of the regular hexahedron (The Sage Developers).
Hexahedral Graph
See also
Cubical Graph, Hexahedron, Polyhedral 6-Vertex Graph, Polyhedral GraphExplore with Wolfram|Alpha
References
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.The Sage Developers. "Common Graphs: HexahedralGraph." SageMath Reference Manual. https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html#sage.graphs.graph_generators.GraphGenerators.HexahedralGraph.Referenced on Wolfram|Alpha
Hexahedral GraphCite this as:
Weisstein, Eric W. "Hexahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HexahedralGraph.html