Given a triangle *T* with sides *a, b,* and *c,* describe its "fitting set," the set of all points (*x,y,z*) in 3-dimensions for which a triangle with sides *x, y, z* exists that fits in *T.*

Such a set lies in the positive octant, is star-shaped with respect to the origin, and probably is a polyhedron; but it seems difficult to describe.