Simplest Canonical Polyhedra of Each Symmetry Type
(box: x-ray)
(F: faces)
(slider: perspective)
(image: L=rotate R=zoom)
(M: metrics)
Please use a browser that supports "canvas"
Simplest Canonical Polyhedron with Ih Symmetry
(Uniform #23)
(Dodecahedron)
(2 of 2)
Vertices:
20 (20[3])
Faces:
12 (regular pentagons)
Edges:
30 (all same length)
Symmetry:
Full Icosahedral (Ih)
Dihedral Angle:
acos(−sqrt(5)/5)
≈116.565051177 degrees
Dual Solid:
Icosahedron
(values below based on midscribed radius = 1)
Edge Length:
3−sqrt(5)
≈0.76393202250021030359
Circumscribed Radius:
(sqrt(15)−sqrt(3))/2
≈1.0704662693192697958
Midscribed Radius:
1
Inscribed Radius:
sqrt(10*(5+sqrt(5)))/10
≈0.85065080835203993218
Volume:
2*(3*sqrt(5)−5)
≈3.41640786499873817846