Their construction is credited to Féodor Loupekine in a 1976 technical report published by Rufus Isaacs.

[1] Loupekine's 1992 doctoral dissertation includes the construction, and attaches Isaac's technical report as an appendix, but this appendix has been redacted from the online version of the dissertation.

This alternation between edge pairs with one or two colors cannot be maintained consistently around an odd cycle of blocks.

The simplest Loupekine snarks are obtained by constructing three blocks from three copies of the Petersen graph, connecting them by pairs of edges into a cycle of three blocks, and using a central graph consisting of a three-leaf star.

There are two graphs of this type, depending on how the pairs of edges connecting consecutive blocks are chosen.