Platonic Solids
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(Uniform #23)
Dodecahedron
Vertices:
20 (20[3])
Faces:
12 (regular pentagons)
Edges:
30
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle:
acos(−sqrt(5)/5)
≈116.565051177 degrees
Dual Solid:
Icosahedron
(values below based on edge length = 1)
Circumscribed Radius:
(sqrt(3)+sqrt(15))/4
≈1.4012585384440735447
Midscribed Radius:
(3+sqrt(5))/4
≈1.3090169943749474241
Inscribed Radius:
sqrt(10*(25+11*sqrt(5)))/20
≈1.1135163644116067352
Volume:
(15+7*sqrt(5))/4
≈7.6631189606246319687