Dipyramids & Trapezohedra

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Octagonal 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(−(2*sqrt(130+79*sqrt(2))−5−6*sqrt(2))/47)    ≈137.370466429 degrees
Dual Solid:  Octagonal Antiprism
(values below based on unit-edge-length Octagonal Antiprism)
Short Edge (16):  sqrt(1−sqrt(2)+sqrt(2−sqrt(2)))    ≈0.59258189506353001187
Long Edge (16):  sqrt(2*(8+5*sqrt(2)+sqrt(2*(58+41*sqrt(2)))))/2    ≈3.89239526906081497849
[3]-Vertex Radius (16):  sqrt(6*(2+sqrt(2*(2+sqrt(2)))))/4    ≈1.31526507733509080496
[8]-Vertex Radius (2):  sqrt(2*(30+20*sqrt(2)    
    +sqrt(2*(850+601*sqrt(2)))))/4    
≈3.8176039854060190482
Edge-scribed Radius:  sqrt(2*(4+2*sqrt(2)+sqrt(2*(10+7*sqrt(2)))))/4    ≈1.2814577238707530894
Inscribed Radius:  sqrt(94*(146+88*sqrt(2)    
    +5*sqrt(2*(706+497*sqrt(2)))))/188    
≈1.1938029096323123057
Volume:2*sqrt(2*(50+35*sqrt(2)    
    +sqrt(4954+3503*sqrt(2))))/3    
≈13.301173285055892044