Question

What is the difference between (i) convex polygons and concave polygons ( ii) polyhedrons and non - polyhedrons. Give example of each.

Answer 1

Concave Polygon	Convex Polygon
Definition	A polygon with one or more interior angles greater than 180 degrees is referred to as a concave polygon.	A polygon of which all interior angles are less than 180 degrees is known as a convex polygon.
Properties	At least one interior angle is greater than 180 degrees It can be cut into a set of convex planes. A polygon that is not a convex polygon is referred to as a concave polygon.	Every internal angle is less than 180 degrees. Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon). Any vertical or horizontal axis intersects it at most twice.
Recognizing feature	A dent (curve inward)	All of its lines curve outside
Distinguishing Feature	A line does contain a side of the polygon containing a point on the interior of the polygon.	No line that contains a side of the polygon contains a point in the interior of the polygon.
Ways to create	Many	Comparatively few
Cross product	Cross product of adjacent vector pairs is <0	Cross-product of adjacent edges will be of same sign (that is, the z-component)
Example	The outline of the letter "W"	Triangle

A polyhedron is a closed figure with several (planar) sides, and all its sides are planar. A non-polyhedron does not have these properties, maybe it is not closed, maybe one or more of the sides is a curved surface. In some branches of topology, the sides of a polyhedron cannot intersect each other.