Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with Oh Symmetry
(Uniform #5)
(Octahedron)
(1 of 2)
Vertices:
6 (6[4])
Faces:
8 (equilateral triangles)
Edges:
12 (all same length)
Symmetry:
Full Octahedral (Oh)
Dihedral Angle:
acos(−1/3)
≈109.471220634 degrees
Dual Solid:
Cube
(values below based on midscribed radius = 1)
Edge Length:
2
Circumscribed Radius:
sqrt(2)/2
≈1.4142135623730950488
Midscribed Radius:
1
Inscribed Radius:
sqrt(6)/3
≈0.81649658092772603273
Volume:
8*sqrt(2)/3
≈3.77123616632825346347