Prisms & Antiprisms

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(Uniform #77) Octagonal Antiprism

Vertices:   16  (16[4]) Faces: 18  (16 equilateral triangles + 2 regular octagons) Edges: 32 Symmetry:   8-fold Antiprismatic  (D8v) Octagon-Triangle Angle:   acos(−sqrt(3*(7+4*sqrt(2)         −2*sqrt(2*(10+7*sqrt(2)))))/3)     ≈96.594518216 degrees Triangle-Triangle Angle:   acos(−(2*sqrt(2+sqrt(2))−1)/3)     ≈153.962382889 degrees Dual Solid:   Octagonal Trapezohedron (values below based on edge length = 1) Circumscribed Radius:   sqrt(2*(6+2*sqrt(2)+sqrt(2*(10+7*sqrt(2)))))/4     ≈1.3755485807735077127 Midscribed Radius:   sqrt(2*(4+2*sqrt(2)+sqrt(2*(10+7*sqrt(2)))))/4     ≈1.2814577238707530894 Octagon Center Radius:   sqrt(2*(sqrt(2*(10+7*sqrt(2)))−2−2*sqrt(2)))/4     ≈0.43014778493148578322 Triangle Center Radius:   sqrt(6*(10+6*sqrt(2)         +3*sqrt(2*(10+7*sqrt(2)))))/12     ≈1.2485193489628736783 Volume: 2*sqrt(4+2*sqrt(2)+2*sqrt(146+103*sqrt(2)))/3     ≈4.2679567504571366708 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).