Re:Leaf

This design is inspired by the appearance of plant cells under a microscope.

Counting the thin, oval-shaped holes in this object in three separate ways reveals some of the fundamental equations underlying the Platonic solids:

Each face contains three ovals (and every oval belongs to exactly one face), giving a total of 3F. There are two ovals per edge, giving a total of 2E. Each vertex is surrounded by five ovals (and every oval belongs to exactly one vertex), giving a total of 5V ovals. 

For a general Platonic solid whose faces have p sides with q faces meeting at each vertex, these equations become pF = 2E = qV. Combined with the Euler characteristic, these equations are instrumental in one proof that the five familiar Platonic solids are in fact the only possible ones.