There is exactly one cubic planar graph with six 3-faces and six 7-faces (and no other faces). Surely it must have a name. What is it called?
Here is a picture of the graph embedded on the plane with a point at infinity:
A slightly more general question: How can I find out what the names are of semi-famous graphs? A graph is semi-famous if it has an established name but is not easily found in a standard textbook on the subject.
I did try the House of Graphs by searching using their drawing tool, but found nothing.