Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with D9h Symmetry
(Enneagonal Dipyramid)
(1 of 2)
Vertices:  11  (9[4] + 2[9])
Faces:18  (isosceles triangles)
Edges:27  (9 short + 18 long)
Symmetry:  9-fold Prismatic  (D9h)
Dihedral Angle:  acos(-root[199*(x^3)−243*(x^2)+69*x−1])    ≈142.236557538 degrees
Dual Solid:  Simplest D9h (2 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (9):  sqrt(root[(x^3)−132*(x^2)+432*x−192])    ≈0.72794046853240472270
Long Edge (18):  sqrt(root[3*(x^3)−144*(x^2)+1536*x−4096])    ≈3.1114476537208246401
[4]-Vertex Radius (9):  root[(x^3)+6*(x^2)−8]    ≈1.0641777724759121408
[9]-Vertex Radius (2):  sqrt(root[3*(x^3)−36*(x^2)+96*x−64])    ≈2.9238044001630872522
Edge-scribed Radius:  1
Inscribed Radius:  sqrt(root[199*(x^3)−420*(x^2)+288*x−64])    ≈0.946188648339465264651
Volume:root[(x^3)+36*(x^2)−1728]    ≈6.3850666348554728449