Dipyramids & Trapezohedra

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Tetragonal Trapezohedron
Vertices:  10  (8[3] + 2[4])
Faces:8  (tri-equiangular kites)
Edges:16  (8 short + 8 long)
Symmetry:  4-fold Antiprismatic  (D4v)
Dihedral Angle:  acos(−(2*sqrt(2)−1)/7)    ≈105.141507814 degrees
Dual Solid:  Square Antiprism
(values below based on unit-edge-length Square Antiprism)
Short Edge (8):  sqrt(sqrt(2)−1)    ≈0.64359425290558262474
Long Edge (8):  sqrt(2*(1+sqrt(2)))/2    ≈1.0986841134678099660
[3]-Vertex Radius (8):  sqrt(6*sqrt(2))/4    ≈0.72823765756098513043
[4]-Vertex Radius (2):  sqrt(2*(4+3*sqrt(2)))/4    ≈1.0150517651282178049
Edge-scribed Radius:  sqrt(2*(2+sqrt(2)))/4    ≈0.65328148243818826393
Inscribed Radius:  sqrt(14*(8+5*sqrt(2)))/28    ≈0.51877375697520513724
Volume:sqrt(4+3*sqrt(2))/3    ≈0.95699998183671671759