Prisms & Antiprisms

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

(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).