In the mathematical field of graph theory

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, a Descartes snark is an undirected graph with 210 vertices and 315 edges. It is a snark

Snark (graph theory)

In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...

, first discovered by William Tutte in 1948 under the pseudonym Blanche Descartes

Blanche Descartes

Blanche Descartes was a collaborative pseudonym used by the English mathematicians R. Leonard Brooks, Arthur Harold Stone, Cedric Smith, and W. T. Tutte. The four mathematicians met in 1935 as undergraduate students at Trinity College, Cambridge, where they joined the Trinity Mathematical Society...

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A Descartes snark is obtained from the Petersen graph

Petersen graph

In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it...

 by replacing each vertex with a nonagon and each edge with a particular graph closely related to the Petersen graph. Because there are multiple ways to perform this procedure, there are multiple Descartes snarks.