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