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.
References:
T. Fowler, (find this reference)
Submitted by: Dan Archdeacon, Dept. of Math. and Stat.,
Send comments to dan.archdeacon@uvm.edu
December, 2003