A snark superposition is a graph construction that starts with a connected cubic graph 
and replaces its vertices and edges by cubic graph
multipoles called supervertices and superedges, respectively. Each supervertex
has three connectors, one for each incident edge of 
, and each superedge is a graph
dipole. Joining corresponding connectors produces a cubic graph that retains
the incidence pattern of 
(Máčajová and Škoviera 2021).
A snark superposition is proper if its base graph is a snark and every superedge is proper. A superedge is proper if, for every nowhere-zero 
-flow on its graph dipole,
the total flow through each connector is nonzero. Every connected proper snark superposition
is a snark (Máčajová and Škoviera 2021).
The Descartes snarks are early examples of proper snark superposition. Their base graph is the Petersen
graph, their supervertices are 9-cycles, and their superedges are proper 
-graph
dipoles obtained by deleting two vertices at distance 2 from the Petersen
graph (Descartes 1948, Máčajová and Škoviera 2021).
