Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with D7h Symmetry
(Heptagonal Dipyramid)
(1 of 2)
Vertices:  9  (7[4] + 2[7])
Faces:14  (isosceles triangles)
Edges:21  (7 short + 14 long)
Symmetry:  7-fold Prismatic  (D7h)
Dihedral Angle:  acos(-root[239*(x^3)−227*(x^2)+45*x−1])    ≈133.089524326 degrees
Dual Solid:  Simplest D7h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (7):  sqrt(root[(x^3)−84*(x^2)+560*x−448])    ≈0.96314923761505728866
Long Edge (14):  sqrt(root[7*(x^3)−224*(x^2)+1792*x−4096])    ≈2.558096015379865211496
[4]-Vertex Radius (7):  root[(x^3)−4*(x^2)−4*x+8]    ≈1.1099162641747423828
[7]-Vertex Radius (2):  sqrt(root[7*(x^3)−56*(x^2)+112*x−64])    
    = 1/sin(π/7)    
≈2.3047648709624865052
Edge-scribed Radius:  1
Inscribed Radius:  sqrt(root[239*(x^3)−472*(x^2)+304*x−64])    ≈0.91737131605281802647
Volume:root[27*(x^3)−504*(x^2)−2352*x+21952]    ≈5.1796092328154644533