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