Typical mirror shapes are planar, convex, and concave. Simple quadrilaterals are either convex or concave. The focal length is positive for a concave mirror, and negative for a convex mirror. Submodular functions have properties which are very similar to convex and concave functions. The kidney is a bean-shaped structure with a convex and a concave border. The throne hall stands on a high base with convex and concave moldings. The surface may be either "convex" (bulging outward) or "concave" (recessed inward). They have convex and concave regions that produce deliberately distorted images. An implementation that keeps separate lists of convex and concave vertices will run in time. Discrete geometry is a subject that has close connections with convex geometry. There are 3 types of monohedral convex hexagonal tilings. Projective polarity works well enough for convex polyhedra. Regular polygons may be either convex or star. Let formula 16 be a smooth regular convex closed curve. Cubes and pyramids are examples of convex polyhedra.