There is no obvious extension of the coloring result to three-dimensional solid regions. By using a set of "n" flexible rods, one can arrange that every rod touches every other rod. The set would then require "n" colors, or "n"+1 if you consider the empty space that also touches every rod. The number "n" can be taken to be any integer, as large as desired. Such examples were known to Fredrick Guthrie in 1880 . Even for axis-parallel cuboids (considered to be adjacent when two cuboids share a two-dimensional boundary area) an unbounded number of colors may be necessary (; ).