Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D4v Symmetry
(Tetragonal Trapezohedron)
(2 of 2)
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:
Simplest D4v (1 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (8):
2*sqrt(3*sqrt(2)−4)
≈0.98517143100941603869
Long Edge (8):
sqrt(2*sqrt(2))
≈1.6817928305074290861
[3]-Vertex Radius (8):
sqrt(3*(sqrt(2)−1))
≈1.1147379454918026367
[4]-Vertex Radius (2):
sqrt(1+sqrt(2))
≈1.5537739740300373073
Edge-scribed Radius:
1
Inscribed Radius:
sqrt(7*(3+sqrt(2)))/7
≈0.794104487760817733346
Volume:
16*sqrt(sqrt(2)−1)/3
≈3.4325026821631073319