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 D5h Symmetry
(Pentagonal Dipyramid)
(1 of 2)
Vertices:
7 (5[4] + 2[5])
Faces:
10 (isosceles triangles)
Edges:
15 (5 short + 10 long)
Symmetry:
5-fold Prismatic (D5h)
Dihedral Angle:
acos(−(11+4*sqrt(5))/41)
≈119.107231366 degrees
Dual Solid:
Simplest D5h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (5):
2*sqrt(5−2*sqrt(5))
≈1.4530850560107217718
Long Edge (10):
2*sqrt(10*(5−sqrt(5)))/5
≈2.1029244484765344241
[4]-Vertex Radius (5):
sqrt(5)−1
≈1.2360679774997896964
[5]-Vertex Radius (2):
sqrt(10*(5+sqrt(5)))/5
≈1.7013016167040798644
Edge-scribed Radius:
1
Inscribed Radius:
sqrt(82*(13+sqrt(5)))/41
≈0.86210372239697553031
Volume:
10*(sqrt(5)−1)/3
≈4.1202265916659656547