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