TITLE: Name of a 6 vertices graph
QUESTION [5 upvotes]: Does this undirected graph with 6 vertices and 9 undirected edges have a name?

I know a few names that are not right. It is not a complete graph because all the vertices are not connected. It is close to K3,3 the utility graph, but not quite (and not quite matters in graph theory :-) 
This graph came up in my analysis of quaternion triple products.

REPLY [2 votes]: You can also think of it as the Harary graph $H_{3,6}$.