Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above shows the technique for each hexahedron.
Tutte's Wheel Theorem
See also
Edge Contraction, Polyhedral Graph, Vertex Contraction, Wheel GraphThis entry contributed by Ed Pegg, Jr. (author's link)
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Pegg, Ed Jr. "Tutte's Wheel Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TuttesWheelTheorem.html