Simplest Canonical Polyhedra of Each Symmetry Type
(box: x-ray)
(F: faces)
(slider: perspective)
(image: L=rotate R=zoom)
(M: metrics)
Please use a browser that supports "canvas"
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