Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C6v Symmetry
(Hexagonal Pyramid)
Vertices:  7  (6[3] + 1[6])
Faces:7  (6 isosceles triangles + 1 regular hexagon)
Edges:12  (6 short + 6 long)
Symmetry:  6-fold Pyramidal  (C6v)
Dual Solid:  Hexagonal Pyramid (itself)
(values below based on edge-scribed radius = 1)
Short Edge (6):  2*sqrt(6*(2*sqrt(3)−3))/3    ≈1.1124766546017998270
Long Edge (6):  2*sqrt(6*(3+2*sqrt(3)))/3    ≈4.1518193972081700163
Edge-scribed Radius:  1
Volume:16*(2−sqrt(3))    ≈4.2871870788979633036