Platonic Solids
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(Uniform #22)
Icosahedron
Vertices:
12 (12[5])
Faces:
20 (equilateral triangles)
Edges:
30
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle:
acos(−sqrt(5)/3)
≈138.189685104 degrees
Dual Solid:
Dodecahedron
(values below based on edge length = 1)
Circumscribed Radius:
sqrt(2*(5+sqrt(5)))/4
≈0.95105651629515357212
Midscribed Radius:
(1+sqrt(5))/4
≈0.80901699437494742410
Inscribed Radius:
(3*sqrt(3)+sqrt(15))/12
≈0.75576131407617073048
Volume:
5*(3+sqrt(5))/12
≈2.181694990624912373504