Properties of an Icosahedron:

• Number of Faces: 20
• Number of Edges: 30
• Number of Vertices: 12
• All faces are equilateral triangles.
• All vertices are equivalent, and all edges have the same length.

Formulas for Icosahedron:

• Icosahedron's Surface Area (A) = 5 * √3 * a²
• Icosahedron's Volume (V) = (5/12) * (3 + √5) * a³
• Where 'a' is the length of the edge of the icosahedron.

Real-World Applications:

The icosahedron appears in nature in the form of viral particles, carbon molecules (C60 buckyballs), and various minerals. It's also used in geodesic dome constructions and as a basis for soccer balls.

Related Concepts:

• Platonic solids
• Polyhedra
• Geometry of 3D shapes