EPI- n.
A prefix, meaning upon, beside, among, on the outside, above, over. It becomes ep- before a vowel, as in epoch, and eph- before a Greek aspirate, as in ephemeral.
PERI- n.
A prefix used to signify around, by, near, over, beyond, or to give an intensive sense; as, perimeter, the measure around; perigee, point near the earth; periergy, work beyond what is needed; perispherical, quite spherical.