Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with D5v Symmetry
(Pentagonal Trapezohedron)
(2 of 2)
Vertices:  12  (10[3] + 2[5])
Faces:10  (tri-equiangular kites)
Edges:20  (10 short + 10 long)
Symmetry:  5-fold Antiprismatic  (D5v)
Dihedral Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Simplest D5v (1 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (10):  3−sqrt(5)    ≈0.76393202250021030359
Long Edge (10):  2
[3]-Vertex Radius (10):  (sqrt(15)−sqrt(3))/2    ≈1.0704662693192697958
[5]-Vertex Radius (2):  sqrt(2*(5+sqrt(5))/2    ≈1.9021130325903071442
Edge-scribed Radius:  1
Inscribed Radius:  sqrt(10*(5+sqrt(5)))/10    ≈0.85065080835203993218
Volume:10*(sqrt(5)−1)/3    ≈4.1202265916659656547