concave
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A concave quadrilateral. An arrowhead or a delta, for example.
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.
If any of the angles is greater than 180 degrees, the quadrilateral is concave.
No. There can be no regular concave polygon.
All angles < 180 degrees are concave. An acute angle is < 90 degrees. So, all acute angles are concave.