English: An apex graph, used by Neil Robertson as an example of a graph that is linklessly embeddable but not YΔY-reducible. It can be formed by connecting a new vertex (the apex, shown in red) to each degree-three vertex of a rhombic dodecahedron, or by merging two opposite vertices of a four-dimensional hypercube graph to form a single supervertex. It is triangle-free and has minimum degree four, preventing any YΔY-reduction from applying to it.