  Vibrated monolayers of granular particles confined into horizontal cavities
form a variety of fluid patterns with orientational order that resemble
equilibrium liquid-crystal phases. In some cases one can identify nematic and
smectic patters that can be understood in terms of classical statistical
mechanics of hard bodies. Low aspect ratio cylinders project as rectangles and
form uniaxial, or 2-atic, and tetratic, or 4-atic, nematic phases. Other
polygonal particles may exhibit different liquid-crystal phases, in general
$p$-atic phases, of higher symmetries. We give a brief summary of theoretical
work on rectangles and triangles, and provide some experimental results on
vibrated monolayers. In the case of equilateral triangles, the theory predicts
an exotic triatic phase, or 6-atic phase, with six-fold symmetry and three
equivalent directors. Right-angled triangles exhibit a 4-atic phase with strong
octatic (8-atic) correlations. Experiments on cylinders show 4-atic textures
and, even more remarkable, geometric frustration caused by confinement excites
topological defects, which seem to follow the same topological rules as
standard liquid crystals. Some of our findings can be understood with the help
of simulations of hard particles subject to thermal equilibrium, although
standard Density-Functional Theories fail to account for the correct
equilibrium phases in some cases.
