Star Dipyramids & Trapezohedra
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Pentagrammic Dipyramid
Vertices:
7 (5[4] + 2[5])
Faces:
10 (isosceles triangles)
Edges:
15 (10 short + 5 long)
Symmetry:
5-fold Prismatic (D5h)
Dihedral Angle:
acos(−(11−4*sqrt(5))/41)
≈92.873998801 degrees
Dual Solid:
Pentagrammic Prism
(values below based on unit-edge-length Pentagrammic Prism)
Short Edge (10):
4*sqrt(5)/5
≈1.7888543819998317571
Long Edge (5):
1+sqrt(5)
≈3.2360679774997896964
[5]-Vertex Radius (2):
(5−sqrt(5))/5
≈0.55278640450004206072
[4]-Vertex Radius (5):
sqrt(10*(5+sqrt(5)))/5
≈1.7013016167040798644
Edge-scribed Radius:
sqrt(10*(5−sqrt(5)))/10
≈0.52573111211913360603
Inscribed Radius:
sqrt(410*(35−9*sqrt(5)))/205
≈0.38095372233513360886