Star Dipyramids & Trapezohedra
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Pentagrammic Trapezohedron
Vertices:
12 (10[3] + 2[5])
Faces:
10 (tri-equiangular kites)
Edges:
20 (10 short + 10 long)
Symmetry:
5-fold Prismatic (D5h)
Dihedral Angle:
acos((4−sqrt(5))/11)
≈80.772355118 degrees
Dual Solid:
Pentagrammic Antiprism
(values below based on unit-edge-length Pentagrammic Antiprism)
Short Edge (10):
sqrt(10*(1+sqrt(5)))/10
≈0.56886448100578310728
Long Edge (10):
sqrt(2*(sqrt(5)−1))/2
≈0.78615137775742328607
[5]-Vertex Radius (2):
sqrt(5*(2+sqrt(5)))/10
≈0.46022103262996301788
[3]-Vertex Radius (10):
sqrt(15*sqrt(5))/10
≈0.57914609264413452871
Edge-scribed Radius:
sqrt(10*(5+sqrt(5)))/20
≈0.42532540417601996609
Inscribed Radius:
sqrt(55*(10+3*sqrt(5)))/110
≈0.275583710533407196497