Cornea conus (cornea Konik) - Keratoconus. This term refers to a congenital or acquired conical shape of the cornea, found on any part of the corneal surface. There are both unilateral and bilateral horny cones or keratoconia. It is often associated with farsightedness, dry eyes, and decreased vision. Sometimes the conical horn causes false conjunctivitis, when there is little visible mucous and lacrimal gland secretions in the pupil. Cone-type corneas can also develop in people who have long-term keratitis sicca.