Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C3v Symmetry
(1 of 2)
Vertices:  7  (1[3] + 3[3] + 3[4])
Faces:7  (1 equilateral triangle + 3 isosceles triangles
    + 3 isosceles trapezoids)
Edges:12  (4 different lengths)
Symmetry:  3-fold Pyramidal  (C3v)
Dual Solid:  Simplest C3v (1 of 2) (itself)
(values below based on edge-scribed radius = 1)
Edge 1 (3):  2*sqrt(2)/3    ≈0.94280904158206336587
Edge 2 (3):  6*sqrt(2)/5    ≈1.6970562748477140586
Edge 3 (3):  4*sqrt(2)/3    ≈1.8856180831641267317
Edge 4 (3):  2*sqrt(2)    ≈2.8284271247461900976
Edge-scribed Radius:  1
Volume:1256/405    ≈3.1012345679012345679