Star Prisms & Antiprisms

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

(Uniform #78) Heptagrammic 7/2 Prism
Vertices:  14  (14[3])
Faces:9  (7 squares + 2 regular 7/2 heptagrams)
Edges:21
Symmetry:  7-fold Prismatic  (D7h)
Heptagram-Square Angle:  acos(0)    90 degrees
Square-Square Angle:  acos(root[8*(x^3)−4*(x^2)−4*x+1])    
    = acos(sin(π/14))    
540/7 degrees
Dual Solid:  Heptagrammic 7/2 Dipyramid
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(root[448*(x^3)−1232*(x^2)+980*x−239])    
    = sqrt(cot(2*π/7)*cot(2*π/7)+2)/2    
≈0.81178257649071064214
Midscribed Radius:  sqrt(root[7*(x^3)−14*(x^2)+7*x−1])    
    = 1/(2*sin(2*π/7))    
≈0.63952400384496630287
Heptagram Center Radius:  1/2    0.5
Square Center Radius:  sqrt(root[448*(x^3)−560*(x^2)+84*x−1])    
    = cot(2*π/7)/2    
≈0.39873669444120198071


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