Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C2v Symmetry
(2 of 2)
Vertices:  7  (2[3] + 4[3] + 1[4])
Faces:6  (2 isosceles triangles + 2 kites + 2 isosceles trapezoids)
Edges:11  (4 different lengths)
Symmetry:  2-fold Pyramidal  (C2v)
Dual Solid:  Simplest C2v (1 of 2)
(values below based on edge-scribed radius = 1)
Edge 1 (2):  sqrt(root[3*(x^3)+170*(x^2)+1859*x−2772])    ≈1.1517194841721881309
Edge 2 (4):  sqrt(root[432*(x^3)+4236*(x^2)+3124*x−33957])    ≈1.5064769527046090918
Edge 3 (1):  sqrt(root[9*(x^3)+23*(x^2)−121*x−231])    ≈1.8612344212370300527
Edge 4 (4):  sqrt(root[4800*(x^3)+61088*(x^2)−265221*x−399168])    ≈2.0864832931690855022
Edge-scribed Radius:  1
Volume:sqrt(root[57600*(x^3)−14035488*(x^2)    
    +759143473*x−5167497027])    
≈2.8164750311775669474