Biscribed Chiral Solids

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Biscribed Propello Octahedron
biscribed form
Vertices:  30  (6[4] + 24[4])
Faces:32  (8 equilateral triangles + 24 irregular tetragons)
Edges:60  (12 short + 24 medium + 24 long)
Symmetry:  Chiral Octahedral  (O)
Short Edge Angle:  acos(-root[108*(x^5)+828*(x^4)    
    +2499*(x^3)+2789*(x^2)−203*x−1789])    
≈129.497883904 degrees
Medium Edge Angle:  acos(-root[27*(x^5)+63*(x^4)    
    +426*(x^3)−382*(x^2)−5*x−1])    
≈142.306571894 degrees
Long Edge Angle:  acos(-root[27*(x^5)−63*(x^4)    
    −39*(x^3)+119*(x^2)+48*x−84])    
≈151.196964524 degrees
Dual Solid:  Biscribed Propello Cube
(values below based on circumscribed radius = 1)
Short Edge (12):  sqrt(root[9*(x^5)−264*(x^4)+4372*(x^3)    
    −26152*(x^2)+51328*x−6272])    
≈0.36153961557249314530
Medium Edge (24):  sqrt(root[3*(x^5)−92*(x^3)    
    −72*(x^2)+1152*x−512])    
≈0.682675645996630395651
Long Edge (24):  sqrt(root[(x^5)−22*(x^4)+316*(x^3)    
    −1544*(x^2)+2688*x−1152])    
≈0.79127680876159661802
Circumscribed Radius:  1
Inscribed Radius:  sqrt(root[27*(x^5)+63*(x^4)    
    +426*(x^3)−382*(x^2)−5*x−1])    
≈0.88954689063516369786
Volume:root[243*(x^5)−31752*(x^4)+1076976*(x^3)    
    −2511936*(x^2)−2061312*x−888832]    
≈3.3010959674915030383


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