Dipyramids & Trapezohedra

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Pentagonal Dipyramid
canonical form
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:  Pentagonal Prism
(values below based on unit-edge-length Pentagonal Prism)
Short Edge (5):  sqrt(5)−1    ≈1.2360679774997896964
Long Edge (10):  4*sqrt(5)/5    ≈1.7888543819998317571
[4]-Vertex Radius (5):  sqrt(10*(5−sqrt(5)))/5    ≈1.0514622242382672121
[5]-Vertex Radius (2):  (5+sqrt(5))/5    ≈1.4472135954999579393
Edge-scribed Radius:  sqrt(10*(5+sqrt(5)))/10    ≈0.85065080835203993218
Inscribed Radius:  sqrt(410*(35+9*sqrt(5)))/205    ≈0.73334922834028986758
Volume:2*sqrt(2*(5+sqrt(5)))/3    ≈2.5361507101204095256