Biscribed Chiral Solids

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Biscribed Propello Cube
biscribed form
Vertices:  32  (8[3] + 24[4])
Faces:30  (6 squares + 24 irregular tetragons)
Edges:60  (24 short + 24 medium + 12 long)
Symmetry:  Chiral Octahedral  (O)
Short Edge Angle:  acos(-root[(x^5)+6*(x^4)    
    +45*(x^3)+12*(x^2)−20*x−8])    
≈133.388408691 degrees
Medium Edge Angle:  acos(-root[3*(x^5)−15*(x^4)    
    +7*(x^3)+48*(x^2)−27])    
≈140.083195107 degrees
Long Edge Angle:  acos(-root[9*(x^5)+87*(x^4)    
    +655*(x^3)+692*(x^2)−534*x−713])    
≈159.170795734 degrees
Dual Solid:  Biscribed Propello Octahedron
(values below based on inscribed radius = 1)
Short Edge (24):  sqrt(root[(x^5)+56*(x^4)+6468*(x^3)    
    −2480*(x^2)+960*x−256])    
≈0.55919602891294044122
Medium Edge (24):  sqrt(root[(x^5)+20*(x^4)+1648*(x^3)    
    +6080*(x^2)+4096*x−4096])    
≈0.72629651761238644392
Long Edge (12):  sqrt(root[(x^5)−12*(x^4)+10729*(x^3)    
    −12412*(x^2)+39152*x−33856])    
≈0.95910726318549441417
Circumscribed Radius:  sqrt(root[(x^5)+5*(x^4)+382*(x^3)    
    −426*(x^2)−63*x−27])    
≈1.1241678325534580897
Inscribed Radius:  1
Volume:root[(x^5)−36*(x^4)+388*(x^3)    
    −992*(x^2)−256*x−2048]    
≈4.7423130642397570220


References:[1]Sculpture Based on Propellorized Polyhedra (George Hart)