Regular Dodecahedron Calculator

The regular dodecahedron is one of the five Platonic solids. Its 12 pentagonal faces contain the golden ratio φ = (1+√5)/2, making it deeply connected to this famous number.

Key Properties:

• 12 regular pentagonal faces
• 30 edges (all equal length)
• 20 vertices (each meets 3 pentagons)
• Dual of the icosahedron
• Dihedral angle: arctan(2) ≈ 116.57°

Golden Ratio Connection:

The pentagon diagonal-to-side ratio is φ. The dodecahedron's dimensions are saturated with golden ratio relationships, making it a symbol of mathematical beauty.