Truncated Archimedean Solids

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Canonical Truncated Truncated Cube
Vertices:  72  (48[3] + 24[3])
Faces:38  (6 quad-symmetric hexadecagons
    + 8 regular hexagons + 24 isosceles triangles)
Edges:108  (48 short + 48 medium + 12 long)
Symmetry:  Full Octahedral  (Oh)
(values below based on edge-scribed radius = 1)
Short Edge (48):  (2−sqrt(2))/3    ≈0.19526214587563498373
Medium Edge (48):  (13−5*sqrt(2))/21    ≈0.28233010419688213124
Long Edge (12):  (4−sqrt(2))/7    ≈0.36939806251812927874
Edge-scribed Radius:  1
Volume:2*(240−109*sqrt(2))/63    ≈2.72541973655024252954