Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with D3 Symmetry
(1 of 2)
Vertices:  11  (6[3] + 3[4] + 2[6])
Faces:12  (6 obtuse triangles + 6 irregular tetragons)
Edges:21  (4 different lengths)
Symmetry:  3-fold Dihedral  (D3)
Dual Solid:  Simplest D3 (2 of 2)
(values below based on edge-scribed radius = 1)
Edge 1 (3):  sqrt(root[(x^3)+716*(x^2)−1680*x+576])    ≈0.64576755876416399248
Edge 2 (6):  sqrt(root[9*(x^3)+1328*(x^2)−9984*x+7056])    ≈0.88895399099519066374
Edge 3 (6):  sqrt(root[9*(x^3)+1824*(x^2)−11008*x+12544])    ≈2.0894490913958305796
Edge 4 (6):  sqrt(root[81*(x^3)−900*(x^2)+2496*x+16])    ≈2.3326355236268572509
Edge-scribed Radius:  1
Volume:sqrt(root[3*(x^3)+1664*(x^2)−102848*x+1364224])    ≈4.46145449879729284753