Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C3 Symmetry
(2 of 5)
Vertices:  11  (1[3] + 1[3] + 3[3] + 3[3] + 3[4])
Faces:9  (3 acute triangles + 3 kites + 3 irregular pentagons)
Edges:18  (5 different lengths)
Symmetry:  3-fold Cyclic  (C3)
Dual Solid:  Simplest C3 (1 of 5)
(values below based on edge-scribed radius = 1)
Edge 1 (3):  sqrt(root[12th-order polynomial])    ≈0.7444579276997718225502
Edge 2 (3):  sqrt(root[12th-order polynomial])    ≈1.16429452894639568652
Edge 3 (6):  sqrt(root[12th-order polynomial])    ≈1.2423522200570259269
Edge 4 (3):  sqrt(root[12th-order polynomial])    ≈1.2814871806041052027
Edge 5 (3):  sqrt(root[12th-order polynomial])    ≈1.3914879754025424638
Edge-scribed Radius:  1
Volume:sqrt(root[12th-order polynomial])    ≈3.1039634067546582620