Plants and animals are built from the regular patterns of nature. If not so, it would be chaos, and many living creatures would be unviable. The geometry is encoded in the genes. DNA chains project a kind of hologram, into which the living creature grows in. If the DNA is damaged (for example by radiation), the geometry will be distorted. Just think about four-leaves clover, which is abnormal.
I made a selection of my original photos, which are good examples to geometry. The first series is about polygons.
Four-petals (cross):
Perfect pentagram:
Hexagram:
Heptagram in a poppy: