Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C2v Symmetry
(1 of 2)
Vertices:  6  (2[3] + 2[4] + 2[4])
Faces:7  (2 isosceles triangles + {2 opposite * 2} obtuse triangles + 1 rhombus)
Edges:11  (4 different lengths)
Symmetry:  2-fold Pyramidal  (C2v)
Dual Solid:  Simplest C2v (2 of 2)
(values below based on edge-scribed radius = 1)
Edge 1 (2):  sqrt(root[11664*(x^3)−4941*(x^2)−51832*x−11088])    ≈1.55600784974703420503
Edge 2 (4):  sqrt(root[27*(x^3)+2017*(x^2)+8096*x−59136])    ≈1.9256946224833503653
Edge 3 (1):  sqrt(root[81*(x^3)+276*(x^2)−1936*x−4928])    ≈2.1491683882523932274
Edge 4 (4):  sqrt(root[1296*(x^3)+32451*(x^2)−220000*x−241472])    ≈2.5188551609887093877
Edge-scribed Radius:  1
Volume:sqrt(root[34012224*(x^3)−210984797331*(x^2)    
    +2866761678880*x−3266701794048])    
≈3.5155958012142648534