Rectified Archimedean Solids

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Rectified Truncated Cube
derived form
Vertices:  36  (24[4] + 12[4])
Faces:38  (6 regular octagons + 8 equilateral triangles
    + 24 isosceles triangles)
Edges:72  (24 short + 48 long)
Symmetry:  Full Octahedral  (Oh)
(values below based on short edge length = 1)
Short Edge (24):  1
Long Edge (48):  sqrt(2+sqrt(2))    ≈1.8477590650225735123
Circumscribed Radius:  2+sqrt(2)    ≈3.4142135623730950488
Volume:2*(81+56*sqrt(2))/3    ≈106.79730632859554849