Simplest Canonical Polyhedra of Each Symmetry Type

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Simplest Canonical Polyhedron with D3 Symmetry
(2 of 2)
Vertices:  12  (6[3] + 6[4])
Faces:11  (6 isosceles triangles + 3 rhombi + 2 triambi)
Edges:21  (18 short + 3 long)
Symmetry:  3-fold Dihedral  (D3)
Dual Solid:  Simplest D3 (1 of 2)
(values below based on edge-scribed radius = 1)
Short Edge (18):  sqrt(root[3*(x^3)−448*(x^2)+2148*x−1764])    ≈1.0243131011105349803
Long Edge (3):  sqrt(root[3*(x^3)−40*(x^2)+144*x−144])    ≈1.3045290077489670001
Edge-scribed Radius:  1
Volume:sqrt(root[3*(x^3)+1089647*(x^2)    
    −54093663*x+344065401])    
≈2.7369529817261621523