Convex
A set in Euclidean space 
is convex set if it contains
all the line segments connecting any pair
of its points. If the set does not contain all the line
segments, it is called concave.
A convex set is always star convex, implying pathwise-connected, which in turn implies connected.
A region can be tested for convexity in the Wolfram Language using the function Region`ConvexRegionQ[reg].
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convex lamina