A convex polyomino (sometimes called a "convex polygon") is a polyomino whose perimeter is equal to that of its minimal bounding box . If it furthemore contains at least one corner of its minimal bounding box, it is said to be a directed convex polyomino. A column-convex polyomino is a self-avoiding polyomino such that the intersection of any vertical line with the polyomino has at most two connected components, and a row-convex polyomino is similarly defined. A number of types of named convex polyominoes are depicted above .

column-convex polyomino | directed convex polyomino | parallelogram polyomino | polyomino | stack polyomino | staircase polygon