Star Prisms & Antiprisms

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(Uniform #80) Pentagrammic Crossed Antiprism
Vertices:  10  (10[4])
Faces:12  (10 equilateral triangles + 2 regular pentagrams)
Edges:20
Symmetry:  5-fold Antiprismatic  (D5v)
Pentagram-Triangle Angle:  acos(sqrt(15*(5+2*sqrt(5)))/15)    ≈37.377368141 degrees
Triangle-Triangle Angle:  acos(sqrt(5)/3)    ≈318.189685104 degrees
Dual Solid:  Pentagrammic Concave Trapezohedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(5−sqrt(5)))/4    ≈0.58778525229247312917
Midscribed Radius:  (sqrt(5)−1)/4    ≈0.30901699437494742410
Pentagram Center Radius:  sqrt(10*(5−sqrt(5)))/20    ≈0.26286555605956680301
Triangle Center Radius:  −(3*sqrt(3)−sqrt(15))/12    ≈−0.11026408970826791628


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.