a triangle has 3 sides, and a circle has 1
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Well, honey, a circle is the shape you're looking for. It's got zero sides, but don't underestimate it just because it's a round little fella. It may not play by the rules of those square and triangle folks, but it's still a valid shape in my book.
Common shapes with less than 4 sides are triangles and circles ( but the circle has no straight sides).
A shape with four sides has four vertices and a shape with three sides has three vertices, so a shape with four sides has more vertices than a shape with three sides.
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A triangle or a circle.
There is no special name that distinguishes shapes with more than four sides from shapes with four or fewer.