Around, near, enclosing
Peri- comes from Greek "peri" (around, near, about) and signals that something surrounds, encloses, or is close to something else: perimeter = measure around a shape; peripheral = at the edges around the centre; periscope = an instrument for seeing around obstacles; pericardium = the membrane around the heart; perihelion = the point in an orbit nearest to (around the closest to) the sun.