Geometry and Platonic Solids

Geometry questions the shape, size, position, and properties of space. Notable accomplishments are formulas for lengths, areas and volumes such as Pythagorean theorem, circumference and area of a circle, triangle, volume of a cylinder and the pyramid.

the theme of symmetry in  geometry is nearly as old as geometry itself. Symmetric patterns occur in nature and were artistically rendered in a multitude of forms including the graphic art of M.C. Escher.

 In geometry a Platonic Solid  is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and angles.

Many viruses, such as the herpes virus, have the shape of a regular icosahedron. Viral structures are built of repeated identical protein subunits and the icosahedron is the easiest shape to assemble using these subunits. A regular polyhedron is used because it can be built from a single basic unit protein used over and over again; this saves space in the viral genome.