With the two rotating calipers algorithm:
http://cgm.cs.mcgill.ca/~orm/rotcal.html
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It is convex if you look at it from the inside but it is not any kind of polygon.
A polygon is convex if you can take any two points inside the polygon and connect them with a line segment that is completely contained by the polygon. A non-convex polygon is one which contains at least two points such that the line joining them does not lie entirely inside the polygon.
No. In a convex polygon, all the internal angles are smaller than 180 degrees.
A convex polygon
A regular polygon.