  Two triples of triangles having pairwise disjoint outlines in 3-space are
called combinatorially isotopic if one triple can be obtained from the other by
a continuous motion during which the outlines of the triangles remain pairwise
disjoint. We conjecture that it can be algorithmically checked if an (ordered
or unordered) triple of triangles is combinatorially isotopic to a triple of
triangles having pairwise disjoint convex hulls. We also conjecture that any
unordered triple of pairwise disjoint triangles in 3-space belongs to one of
the 5 types of such triples listed in the paper. We present an elementary proof
that triples of different types are not combinatorially isotopic.
