A length or strand of resilient material is formed into a continuous ring having multiple tissue-engaging portions for engaging and spreading eyeball tissue segments apart. The strand is formed with elongated straight sides joined by corner portions which are enlarged in directions transverse to the length dimension of each adjacent side. The corner portions constitute the tissue-engaging portions and have top and bottom sections and a connecting section that forms a gap for receiving the tissue. Each side of the ring extends from a bottom section of one corner to a top section of an adjacent corner. When the ring is deployed, the tissue is captured in the gaps at the corners of the ring and also is engaged along each side as that side transitions from a position situated below the tissue to a position situated above the issue.