The 
-double
cone graph is the name used in this work for the graphs
that geometrically correspond to a double cone obtained
by connecting all vertices of two 
cycle graphs (each corresponding
with one nappe) with a single additional point. The 
-double cone graph therefore has 
vertices.
The 3-double cone graph is isomorphic to the 
-windmill graph.
Double cone graphs are unit-distance graphs and planar graphs, as illustrated in the first and third sets of drawings above, respectively.
The 3-double cone graph is an outer-cylindrical forbidden minor 
(No. 6; Archdeacon et al. 2001).
