Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C9v Symmetry
(Enneagonal Pyramid)
Vertices:  10  (9[3] + 1[9])
Faces:10  (9 isosceles triangles + 1 regular enneagon)
Edges:18  (9 short + 9 long)
Symmetry:  9-fold Pyramidal  (C9v)
Dual Solid:  Enneagonal Pyramid (itself)
(values below based on edge-scribed radius = 1)
Short Edge (9):  sqrt(root[(x^3)+72*(x^2)+960*x−512])    ≈0.71653484200511640331
Long Edge (9):  sqrt(root[(x^3)−24*(x^2)−384*x−512])    ≈5.9406896083264763268
Edge-scribed Radius:  1
Volume:root[(x^3)−72*(x^2)+1152*x−4608]    ≈6.18654722475458027351