  We conducted a polarimetric observation of the fast-rotating near-Earth
asteroid (1566) Icarus at large phase (Sun-asteroid-observer's) angles
$\alpha$= 57 deg--141deg around the 2015 summer solstice. We found that the
maximum values of the linear polarization degree are
$P_\mathrm{max}$=7.32$\pm$0.25 % at phase angles of
$\alpha_\mathrm{max}$=124$\pm$8 deg in the $V$-band and
$P_\mathrm{max}$=7.04$\pm$0.21 % at $\alpha_\mathrm{max}$=124$\pm$6 deg in the
$R_\mathrm{C}$-band. Applying the polarimetric slope-albedo empirical law, we
derived a geometric albedo of $p_\mathrm{V}$=0.25$\pm$0.02, which is in
agreement with that of Q-type taxonomic asteroids. $\alpha_\mathrm{max}$ is
unambiguously larger than that of Mercury, the Moon, and another near-Earth
S-type asteroid (4179) Toutatis but consistent with laboratory samples with
hundreds of microns in size. The combination of the maximum polarization degree
and the geometric albedo is in accordance with terrestrial rocks with a
diameter of several hundreds of micrometers. The photometric function indicates
a large macroscopic roughness. We hypothesize that the unique environment
(i.e., the small perihelion distance $q$=0.187 au and a short rotational period
of $T_\mathrm{rot}$=2.27 hours) may be attributed to the paucity of small
grains on the surface, as indicated on (3200) Phaethon.
