The hemicubical graph is the skeleton of the hemicube. It has 7 vertices, 11 edges, and 6 faces.
It is implemented in the Wolfram Language as GraphData["HemicubicalGraph"].
Hemicubical Graph
See also
Hemicube, HexahedronExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Hemicubical Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HemicubicalGraph.html