Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with Ih Symmetry
(Uniform #22) (Icosahedron)
(1 of 2)
Vertices:  12  (12[5])
Faces:20  (equilateral triangles)
Edges:30  (all same length)
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(−sqrt(5)/3)    ≈138.189685104 degrees
Dual Solid:  Dodecahedron
(values below based on midscribed radius = 1)
Edge Length:  sqrt(5)−1    ≈1.2360679774997896964
Circumscribed Radius:  sqrt(2*(5−sqrt(5)))/2    ≈1.1755705045849462583
Midscribed Radius:  1
Inscribed Radius:  (sqrt(3)+sqrt(15))/6    ≈0.934172358962715696451
Volume:10*(sqrt(5)−1)/3    ≈4.1202265916659656547