Archimedean Solids

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(Uniform #12) Snub Cube (dextro)
Vertices:  24  (24[5])
Faces:38  (32 equilateral triangles + 6 squares)
Edges:60
Symmetry:  Chiral Octahedral  (O)
Square-Triangle Angle:  acos(−sqrt(11−2*cbrt(17+3*sqrt(33))    
    −2*cbrt(17−3*sqrt(33)))/3)    
≈142.983430074 degrees
Triangle-Triangle Angle:  acos(−sqrt(3*(11+4*cbrt(17+3*sqrt(33))    
    +4*cbrt(17−3*sqrt(33))))/9)    
≈153.234587713 degrees
Dual Solid:  Pentagonal Icositetrahedron (laevo)
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(3*(10+cbrt(199+3*sqrt(33))    
    +cbrt(199−3*sqrt(33))))/6    
≈1.3437133737446017013
Midscribed Radius:  sqrt(3*(7+cbrt(199+3*sqrt(33))    
    +cbrt(199−3*sqrt(33))))/6    
≈1.2472231679936432518
Square Center Radius:  sqrt(3*(4+cbrt(199+3*sqrt(33))    
    +cbrt(199−3*sqrt(33))))/6    
≈1.14261350892596209348
Triangle Center Radius:  sqrt(3*(6+cbrt(199+3*sqrt(33))    
    +cbrt(199−3*sqrt(33))))/6    
≈1.2133558000218923103
Volume:sqrt(188+cbrt(3*(2149479+15037*sqrt(33)))    
    +cbrt(3*(2149479−15037*sqrt(33))))/3    
≈7.889477399975390206451