Biscribed Non-Chiral Solids

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Biscribed Truncated Icosidodecahedron
biscribed form
Vertices:  120  (120[3])
Faces:62  (30 rectangles + 20 ditrigons + 12 dipentagons)
Edges:180  (60 short + 60 medium + 60 long)
Symmetry:  Full Icosahedral  (Ih)
Short Edge Angle:  acos(−sqrt(15*(5+2*sqrt(5)))/15)    ≈142.622631859 degrees
Medium Edge Angle:  acos(−sqrt(10*(5+sqrt(5)))/10)    ≈148.282525589 degrees
Long Edge Angle:  acos(−(sqrt(3)+sqrt(15))/6)    ≈159.094842552 degrees
Dual Solid:  Biscribed Disdyakis Triacontahedron
(values below based on inscribed radius = 1)
Short Edge (60):  (4−3*sqrt(3)+4*sqrt(5)−sqrt(15)    
    −sqrt(2*(5+sqrt(5))))/2    
≈0.0354550379522478657047
Medium Edge (60):  sqrt(3)−3−sqrt(5)+sqrt(15)    ≈0.36896617627650448230
Long Edge (60):  sqrt(2*(5+sqrt(5)))−sqrt(5)−1    ≈0.56815808768082459206
Circumscribed Radius:  sqrt(13−4*sqrt(3)+4*sqrt(5)    
    −2*sqrt(15)−2*sqrt(5+2*sqrt(5)))    
≈1.05581007428339545847
Inscribed Radius:  1
Volume:10*(8−11*sqrt(3)+4*sqrt(5)−3*sqrt(15)    
    +sqrt(2*(1705−900*sqrt(3)    
    +707*sqrt(5)−420*sqrt(15))))    
≈4.4324836253368968103