A normal 2-D quadrilateral would be neither convex or concave. There are three-dimensional quadrilaterals, such as prisms, but it would depend on the shape.
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concave
A concave quadrilateral. An arrowhead or a delta, for example.
If any of the angles is greater than 180 degrees, the quadrilateral is concave.
No. There can be no regular concave polygon.
The sum of the interior angles of a quadrilateral is 360 degrees (not 180). The sum of the exterior angles is also 360 degrees. Whether the quadrilateral is convex or concave is not relevant.