  Solid state physics and quantum electrodynamics with its ultra-relativistic
(massless) particles meet, to their mutual beneit, in the electronic properties
of one-dimensional carbon nanotubes as well as two-dimensional graphene or
surfaces of topological insulators. However, clear experimental evidence for
electronic states with conical dispersion relations in all three dimensions,
conceivable in certain bulk materials, is still missing. In the present work,
we fabricate and study a zinc-blend crystal, HgCdTe, at the point of the
semiconductor-to-semimetal topological transition. Three-dimensional massless
electrons with a velocity of about 10$^6$ m/s are observed in this material, as
testifed by: (i) the dynamical conductivity which increases linearly with the
photon frequency, (ii) in a magnetic field $B$, by a $\sqrt{B}$ dependence of
dipole-active inter-Landau-level resonances and (iii) the spin splitting of
Landau levels, which follows a $\sqrt{B}$ dependence, typical of
ultra-relativistic particles but not really seen in any other electronic system
so far.
