Rectified Archimedean Solids

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Rectified Snub Dodecahedron (laevo)
derived form
Vertices:  150  (60[4] + 60[4] + 30[4])
Faces:152  (12 regular pentagons + 60 mirror-symmetric pentagons
    + 80 equilateral triangles)
Edges:300  (240 short + 60 long)
Symmetry:  Chiral Icosahedral  (I)
(values below based on short edge length = 1)
Short Edge (240):  1
Long Edge (60):  (1+sqrt(5))/2    ≈1.6180339887498948482
Circumscribed Radius:  sqrt(root[(x^6)−21*(x^5)    
    +64*(x^4)−73*(x^3)    
    +39*(x^2)−10*x+1])    
≈4.1941076705041759848
Volume:sqrt(root[6th-order polynomial])    ≈291.165637189697926147