The first (called the "Blanuša double" by Orbanić et al. 2004) and second (called the "Blanuša snark" by Orbanić et al. 2004) Blanuša snarks were the second and third snarks discovered, found by Blanuša (1946). Tutte wrote of the result, "I saw Blanuša's paper soon after it appeared. Alas, I did not understand the language, but the diagram made all clear!" The Blanuša snarks each have 18 vertices and edge chromatic number 4.
The Blanuša snarks are illustrated above in three-dimensional embeddings due to Orbanić et al. (2004). Orbanić et al. (2004) also showed that the first Blanuša snark is of graph genus 2 (i.e., is double-toroidal), which the second has graph genus 1 (i.e., is toroidal).
The Blanuša snarks are used as the logo for the Croatian Mathematical Society (Ivanšić).
The Blanuša snarks are implemented in the Wolfram Language as GraphData[
"BlanusaSnark", 
n, k
]
for 
to 4 and 
,
2, with the original two Blanuša snarks corresponding to 
.
The plots above show the adjacency, incidence, and distance matrices of the first (top) and second (bottom) Blanuša snarks.
The first Blanuša snark was found independently in the embedding shown above by Collier and Schmeichel (1978) who erroneously characterized it as a "new cubic hypohamiltonian graph."
The "first and second Blanuša snarks" are actually the smallest member of two infinite families of snarks of order 
, i.e., Blanuša snarks of type 1 and 2 on 18, 26,
34, 42, ... vertices (Read and Wilson 1998, p. 280), illustrated above.
