Uniquely Colorable Polyhedra
John Conway notes that the dodecahedron has a unique face
4-coloring up to symmetry. Similarly, the tetrahedron has a unique face
4-coloring up to symmetry. The property is preserved if we (repeatedly) truncate
any vertex of the polyhedron of degree 3.
Question: Are these the only polyhedra with unique 4-colorings up to symmetry?
It is known that any cubic polyhedron that is uniquely 4-colorable (not just unique up to symmetry) arises from a truncation of a tetrahedron.
T. Fowler, (find this reference)
Submitted by: Dan Archdeacon, Dept. of Math. and Stat.,
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