  For the Thurston (asymmetric) metric on Teichm\"uller space, the deficiency
from being uniquely geodesic is described by the envelope, defined as the union
of geodesics from the initial point to the terminal point.
  Using the harmonic stretch lines we defined recently, we describe the shape
of envelopes as a cone over a cone over a space, defined from a topological
invariant of the initial and terminal points. We prove that envelopes vary
continuously with their endpoints. We also provide a parametrization of
out-envelopes and in-envelopes in terms of straightened measured laminations
complementary to the prescribed maximally stretched laminations.
  We extend most of these results to the metrically infinite envelopes which
have a terminal point on the Thurston boundary, illustrating some of the
nuances of these with examples, and describing the accumulation set. Finally,
we develop a new characterization of harmonic stretch lines that avoids a
limiting process.
