Star Dipyramids & Trapezohedra

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Octagrammic Trapezohedron
Vertices:  18  (16[3] + 2[8])
Faces:16  (tri-equiangular kites)
Edges:32  (16 short + 16 long)
Symmetry:  8-fold Antiprismatic  (D8v)
Dihedral Angle:  acos((5+6*sqrt(2)−2*sqrt(130−79*sqrt(2)))/47)    ≈83.9729196546 degrees
Dual Solid:  Octagrammic Antiprism
(values below based on unit-edge-length Octagrammic Antiprism)
Short Edge (16):  sqrt(2*(8−5*sqrt(2)−sqrt(2*(58−41*sqrt(2)))))/2    ≈0.60959947759904659527
Long Edge (16):  sqrt(1+sqrt(2)−sqrt(2+sqrt(2)))    ≈0.75263171428695558028
[8]-Vertex Radius (2):  sqrt(2*(30−20*sqrt(2)    
    +sqrt(2*(850−601*sqrt(2)))))/4    
≈0.50686344129911338261
[3]-Vertex Radius (16):  sqrt(6*(2−sqrt(2*(2−sqrt(2)))))/4    ≈0.58660286812318967872
Edge-scribed Radius:  sqrt(2*(4−2*sqrt(2)+sqrt(2*(10−7*sqrt(2)))))/4    ≈0.44998811156820785232
Inscribed Radius:  sqrt(94*(146−88*sqrt(2)    
    +5*sqrt(2*(706−497*sqrt(2)))))/188    
≈0.30102178243630207303