Archimedean Solids

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(Uniform #29) Snub Dodecahedron (laevo)
canonical form
Vertices:  60  (60[5])
Faces:92  (80 equilateral triangles + 12 regular pentagons)
Edges:150
Symmetry:  Chiral Icosahedral  (I)
Pentagon-Triangle Angle:  acos(−sqrt(15*(4*((1/x)−x)*(3*phi+1)    
    +(12*phi+19)))/15)    
≈152.929920276 degrees
Triangle-Triangle Angle:  acos(−(2*(x^2)−3)/3)    ≈164.175366056 degrees
where:  phi = (1+sqrt(5))/2
x = cbrt((phi+sqrt(phi−5/27))/2)+cbrt((phi−sqrt(phi−5/27))/2)
Dual Solid:  Pentagonal Hexecontahedron (dextro)
(values below based on edge length = 1)
Circumscribed Radius:  phi*sqrt(x*(x+phi)+(3-phi))/2    ≈2.1558373751156397018
Midscribed Radius:  phi*sqrt(x*(x+phi)+1)/2    ≈2.0970538352520879924
Pentagon Center Radius:  sqrt(20*(5*(x+(1/x))*(2*phi+1)    
    +(11*phi+12)))/20    
≈1.9809159472818407390
Triangle Center Radius:  x*phi*sqrt(3*(x*(x+phi)+1))/6    ≈2.0770896597432085994
Volume:sqrt(5*(3*(x^2)*(201*phi+157)    
    +21*x*(58*phi+31)+209*(3*phi+2)))/6    
≈37.616649962733362976