Derived Solids

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Tetrahedrally Expanded Tetrated Dodecahedron (canonical)
canonical form
Vertices:  48  (24[4] + 12[4] + 12[4])
Faces:50  ({4 * 2} equilateral triangles + 12 isosceles triangles
    + 6 squares + 12 isosceles trapezoids
    + 12 mirror-symmetric pentagons)
Edges:96  (5 different lengths)
Symmetry:  Full Tetrahedral  (Td)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  sqrt(root[19321*(x^5)−462520*(x^4)
   +3777760*(x^3)−10985984*(x^2)
   +2355456*x−18432])    
≈0.47290019393785839158
Edge 2 (24):  sqrt(root[126765081*(x^5)
   −1063106802*(x^4)
   +1727599168*(x^3)
   −1168221120*(x^2)
   +350717696*x−37601792])    
≈0.49893365134747130092
Edge 3 (24):  sqrt(root[6561*(x^5)−47088*(x^4)
   +122464*(x^3)−194304*(x^2)
   +164096*x−32768])    
≈0.524967108757084210254
Edge 4 (24):  sqrt(root[112593321*(x^5)
   −1016019234*(x^4)
   +3416454208*(x^3)
   −5223418624*(x^2)
   +3365978112*x−601628672])    
≈0.52892531240632894679
Edge 5 (12):  sqrt(root[17161*(x^5)−177208*(x^4)
   +850144*(x^3)−2451968*(x^2)
   +696576*x−18432])    
≈0.53288351605557368332
Edge-scribed Radius:  1
Volume:sqrt(root[5th-order polynomial])    ≈3.9902915467932998012


References:[1]Jim McNeill: Near Misses based on dodecahedra