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