Prisms & Antiprisms

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(Uniform #77) Square Antiprism
Vertices:  8  (8[4])
Faces:10  (8 equilateral triangles + 2 squares)
Symmetry:  4-fold Antiprismatic  (D4v)
Square-Triangle Angle:  acos(−(sqrt(6)−sqrt(3))/3)    ≈103.836160479 degrees
Triangle-Triangle Angle:  acos(−(2*sqrt(2)−1)/3)    ≈127.551602906 degrees
Dual Solid:  Tetragonal Trapezohedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(4+sqrt(2)))/4    ≈0.82266438800803628873
Midscribed Radius:  sqrt(2*(2+sqrt(2)))/4    ≈0.65328148243818826393
Square Center Radius:  sqrt(2*sqrt(2))/4    ≈0.42044820762685727152
Triangle Center Radius:  sqrt(6*(4+3*sqrt(2)))/12    ≈0.58604040983818133611
Volume:sqrt(4+3*sqrt(2))/3    ≈0.95699998183671671759

References:[1]Johannes Kepler, Harmonices Mundi (1619).
[2]Johannes Kepler with E. J. Aiton, A. M. Duncan,
and J. V. Field, translators, The Harmony of the World,
American Philosophical Society (1997).