Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C3 Symmetry
(1 of 5)
Vertices:  9  (3[3] + 3[4] + 3[5])
Faces:11  ({1 + 1} equilateral triangles + 3 isosceles triangles
    + 3 obtuse triangles + 3 irregular tetragons)
Edges:18  (5 different lengths)
Symmetry:  3-fold Cyclic  (C3)
Dual Solid:  Simplest C3 (2 of 5)
(values below based on edge-scribed radius = 1)
Edge 1 (3):  sqrt(root[12th-order polynomial])    ≈1.0620319330769333613
Edge 2 (6):  sqrt(root[12th-order polynomial])    ≈1.3440716787175049274
Edge 3 (3):  sqrt(root[12th-order polynomial])    ≈1.5536433675564391204
Edge 4 (3):  sqrt(root[12th-order polynomial])    ≈1.8356831131970106866
Edge 5 (3):  sqrt(root[12th-order polynomial])    ≈2.1177228588375822527
Edge-scribed Radius:  1
Volume:sqrt(root[12th-order polynomial])    ≈3.7440814913943196357