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