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. Conway asks:

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., University of Vermont, Burlington, VT 05401-1455 USA

Send comments to dan.archdeacon@uvm.edu

December, 2003