  We study two notions. One is that of spindle convexity. A set of circumradius
not greater than one is spindle convex if, for any pair of its points, it
contains every short circular arc of radius at least one, connecting them. The
other objects of study are bodies obtained as intersections of finitely many
balls of the same radius, called ball-polyhedra. We find analogues of several
results on convex polyhedral sets for ball-polyhedra.
