Rectified Archimedean Solids

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Rectified Truncated Cuboctahedron
derived form
Vertices:  72  (24[4] + 24[4] + 24[4])
Faces:74  (6 regular octagons + 8 regular hexagons
    + 12 squares + {24 * 2} acute triangles)
Edges:144  (48 short + 48 medium + 48 long)
Symmetry:  Full Octahedral  (Oh)
(values below based on short edge length = 1)
Short Edge (48):  1
Medium Edge (48):  sqrt(6)/2    ≈1.2247448713915890491
Long Edge (48):  sqrt(2*(2+sqrt(2)))/2    ≈1.3065629648763765279
Circumscribed Radius:  sqrt(3*(2+sqrt(2)))    ≈3.2004125807650621011
Volume:56+43*sqrt(2)    ≈116.81118318204308710