Dipyramids & Trapezohedra

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Pentagonal Trapezohedron
Vertices:  12  (10[3] + 2[5])
Faces:10  (tri-equiangular kites)
Edges:20  (10 short + 10 long)
Symmetry:  5-fold Antiprismatic  (D5v)
Dihedral Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Pentagonal Antiprism
(values below based on unit-edge-length Pentagonal Antiprism)
Short Edge (10):  (sqrt(5)−1)/2    ≈0.61803398874989484820
Long Edge (10):  (1+sqrt(5))/2    ≈1.6180339887498948482
[3]-Vertex Radius (10):  sqrt(3)/2    ≈0.86602540378443864676
[5]-Vertex Radius (2):  sqrt(5+2*sqrt(5))/2    ≈1.5388417685876267013
Edge-scribed Radius:  (1+sqrt(5))/4    ≈0.80901699437494742410
Inscribed Radius:  sqrt(5*(5+2*sqrt(5)))/10    ≈0.68819096023558676910
Volume:5*(3+sqrt(5))/12    ≈2.181694990624912373504