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