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