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http://simplydifferently.org/Geodesic_Dome_Notes?page=3#The

The Icosahedron

Icosahedron

• Uniform Polyhedron: U22
• Platonic Solid
• Platonic Element: Water
• Vertices: 12
• Edges: 30
• Faces: 20
• Wythoff symbol: 5|2 3
• Symmetry Group: icosahedral
• Vertex Configuration: {3, 3, 3, 3, 3}
• Dual: dodecahedron
• V: s³ * 5/12 * (3 + √5)
• A: s² * 20 / 4 * √3
• r_inner: s / 12 * (3 * √3 + √15)
• r_outer: s / 4 * √(10 + 2 * √5)
• 

s = , V = , A = , r_inner = , r_outer = , r_avg =