Biscribed Chiral Solids

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Biscribed Propello Tetrahedron
biscribed form
Vertices:  16  (4[3] + 12[4])
Faces:16  (4 equilateral triangles + 12 irregular tetragons)
Edges:30  (12 short + 6 medium + 12 long)
Symmetry:  Chiral Tetrahedral  (T)
Short Edge Angle:  acos(-root[9*(x^5)+39*(x^4)    
    +130*(x^3)+54*(x^2)−27*x−13])    
≈117.071984442 degrees
Medium Edge Angle:  acos(-root[27*(x^5)+189*(x^4)    
    +606*(x^3)+618*(x^2)−105*x−311])    
≈126.578204616 degrees
Long Edge Angle:  acos(-root[81*(x^5)−189*(x^4)    
    −126*(x^3)+414*(x^2)+93*x−209])    
≈138.621170784 degrees
Dual Solid:  Biscribed Propello Tetrahedron (itself)
(values below based on circumscribed radius = 1)
Short Edge (12):  sqrt(root[81*(x^5)−432*(x^4)−288*(x^3)    
    +2304*(x^2)+3072*x−2048])    
≈0.70660402902513360909
Medium Edge (6):  sqrt(root[27*(x^5)−648*(x^4)+6528*(x^3)    
    −30720*(x^2)+61440*x−32768])    
≈0.89897782053689887509
Long Edge (12):  sqrt(root[9*(x^5)−168*(x^4)+1504*(x^3)    
    −6144*(x^2)+10752*x−6144])    
≈1.0439256956066032646
Circumscribed Radius:  1
Inscribed Radius:  root[27*(x^5)+27*(x^4)    
    +30*(x^3)−42*(x^2)−9*x−1]    
≈0.79795971954568180978
Volume:sqrt(root[14348907*(x^5)−2906155584*(x^4)    
    +210175451136*(x^3)−1364517715968*(x^2)    
    −12834570240*x−1073741824])    
≈2.6814890651712673290


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