Rectified Archimedean Solids

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Rectified Snub Cube (laevo)
derived form
Vertices:  60  (24[4] + 24[4] + 12[4])
Faces:62  (24 mirror-symmetric pentagons + 6 squares
    + 32 equilateral triangles)
Edges:120  (96 short + 24 long)
Symmetry:  Chiral Octahedral  (O)
(values below based on short edge length = 1)
Short Edge (96):  1
Long Edge (24):  sqrt(2)    ≈1.4142135623730950488
Circumscribed Radius:  sqrt(3*(7+cbrt(199+3*sqrt(33))    
    +cbrt(199−3*sqrt(33))))/3    
≈2.49444633598728650354
Volume:sqrt(9808+cbrt(946005042176    
    +2755642368*sqrt(33))    
    +cbrt(946005042176    
    −2755642368*sqrt(33)))/3    
≈57.194349268844263869