It appears again in Book IV of the Elements with regard to the construction of regular polygons. It provides the framework for the richly harmonic pentagram. It is visible in the sand dollar, the starfish and the sea urchin, just to name a few.
Flowers often bloom into pentagonal shapes.
The pentagon can even be found on the insides of fruits and vegetables. The regular pentagon had a particular appeal to the early Pythagoreans, and became the sign of recognition of the society. The proportions of the pentagon are interrelated with the Fibonacci sequence of numbers. If the measure of one side of a pentagon is a Fibonacci number, then the measure of its diagonals the next number in the sequence. Furthermore, the diagonals intersect into Fibonacci proportions.