There are two entities which embody the 4CT; ie
1. A triangulation (G)and
2 A 3-regular map/cubic planar graph (C).
FACT: G is the face-vertex dual of C; and C is the f-v dual of G.
FACT: G is a simple loopless triangulation.
FACT: Every vertex in G has degree = > 5.
FACT: C is a triangle-free 2-connected cubic planar graph
FACT: If C is 3 edge colorable, then the 4CT is true.
If C is not 3 EC, then C is a "snark".
If C is planar, then the 4CT is false
If C is not-planar, the 4CT is false.
CONJECTURE: If