The twinplex graph is the graph illustrated above in a number of embeddings which corresponds to the graph labeled 
in Fischer and Little (2011). It is a cubic Hamiltonian graph on 12 vertices with graph
crossing number 2 and has maximal girth among all 12-vertex cubic graphs (Clancy
et al. 2019). (There are two such graphs with maximal girth 5, the other being
the twinplex graph of Robertson et al. 2019.) The twinplex graph has LCF
notation ![[-5,-4,4,-4,4,5,-4,5,-4,4,-5,4]](/images/equations/TwinplexGraph/Inline2.svg)
.
Norine and Thomas (2008) use the term "twinplex" to refer to one of the 12-vertex cubic graphs 
and 
from Fischer and Little (2001). Unfortunately, in the
figure supposedly giving embeddings for the graphs termed cubeplex
and twinplex in that paper (reproduced above), both embeddings correspond to Fischer
and Little's 
,
which is the cubeplex graph.
