Nontrivial convexity

few examples of nontrivial convexity

Tetragons

by  Ed Pegg Jr

Pentagons

Next images (my results)
by John Wallace (first image is mine)

Next images (my results)
by Michael Hirschhorn (first image by Ed Pegg Jr)

by Karl Scherer	by William Rex Marshall	by Ed Pegg Jr

another nice examples are at Michael Reid's site