Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C3v Symmetry
(2 of 2)
Vertices:  7  (1[3] + 3[3] + 3[4])
Faces:7  (1 equilateral triangle + 3 isosceles triangles
    + 3 kites)
Edges:12  (3 short + 6 medium + 3 long)
Symmetry:  3-fold Pyramidal  (C3v)
Dual Solid:  Simplest C3v (2 of 2) (itself)
(values below based on edge-scribed radius = 1)
Short Edge (3):  (3*sqrt(30)−5*sqrt(6))/3    ≈1.3947426704130309709
Medium Edge (6):  2*(3*sqrt(30)−5*sqrt(6))/5    ≈1.6736912044956371651
Long Edge (3):  2*sqrt(30)/5    ≈2.1908902300206644538
Edge-scribed Radius:  1
Volume:4*(45−11*sqrt(5))/25    ≈3.2645203596003701343