A constructive characterization of 3-connected triangle-free graphs

We present a method to construct the class C of finite simple 3-connected triangle-free graphs from the 3-regular complete bipartite graph K3,3 and the skeleton of a 3-dimensional cube by sequentially applying one of five operations without leaving C in the intermediate steps. Each of these operations can be considered as a sequence of at most six vertex splittings and edge additions.