Convex, concave or something else?

In order to be concave , a polygon must have an angle greater than $180°$ .

This cannot be the case for a circle as it is convex on its circumference.

In a triangle the angles add up to $180°$ so no one angle can be greater than $180°$ so it is convex .

The angles is a square are $90°$ so it is convex .

Finally, angles in a pentagon add up to $540°$ so clearly it can be concave for example the $5$ angles being $200°,100°,80°,80°,80°$ .

$\color{#20A900}{\boxed{\boxed{\text{Pentagon}}}}$