Simplest Canonical Polyhedra of Each Symmetry Type
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Simplest Canonical Polyhedron with D10h Symmetry
(Decagonal Dipyramid)
(1 of 2)
Vertices:
12 (10[4] + 2[10])
Faces:
20 (isosceles triangles)
Edges:
30 (10 short + 20 long)
Symmetry:
10-fold Prismatic (D10h)
Dihedral Angle:
acos(−(15+4*sqrt(5))/29)
≈145.655924299 degrees
Dual Solid:
Simplest D10h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (10):
2*sqrt(5*(5−2*sqrt(5)))/5
≈0.64983939246581265231
Long Edge (20):
2*sqrt(10*(5+sqrt(5)))/5
≈3.4026032334081597287
[4]-Vertex Radius (10):
sqrt(10*(5−sqrt(5)))/5
≈1.0514622242382672121
[10]-Vertex Radius (2):
1+sqrt(5)
≈3.2360679774997896964
Edge-scribed Radius:
1
Inscribed Radius:
sqrt(58*(11+sqrt(5)))/29
≈0.95542256322023833806
Volume:
4*sqrt(10*(5−sqrt(5)))/3
≈7.0097481615884480803