Rectified Archimedean Solids

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Rectified Truncated Octahedron
derived form
Vertices:  36  (24[4] + 12[4])
Faces:38  (8 regular hexagons + 6 squares
    + 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(6)/2    ≈1.2247448713915890491
Circumscribed Radius:  3*sqrt(2)/2    ≈2.1213203435596425732
Volume:31  [EXACT]